Filed by Envision Healthcare Holdings, Inc.

Pursuant to Rule 425 under the Securities Act of 1933, as amended

and deemed filed pursuant to Rule 14a-12

under the Securities Exchange Act of 1934, as amended

Subject Company: Envision Healthcare Holdings, Inc.

Commission File No. 001-36048

[provided to Sheridan & EmCare Leadership on October 4, 2016]

Subject: Merger Integration Planning Update: Physician Services

As our anticipated closing date of the Envision Healthcare and AMSURG merger approaches, we thought this would be a good time to update our leaders on the status of our integration planning for physician services. Below we have detailed progress on a few work streams that are specific to the post-closing integration of EmCare and Sheridan. As a reminder, until closing our organizations remain independent and will conduct business as usual.  While we’re excited about the integration planning progress discussed in this communication, we cannot take steps to implement any of the work stream outputs prior to closing.

When the merger was announced, we shared our vision to be the most trusted strategic partner for providers, health systems, communities and payors in the common pursuit of delivering the highest quality of care for the patients we serve. To deliver on that in our future-state physician services organization, a steering committee comprised of senior leaders from both Sheridan and EmCare has developed the following guiding principles that will aid our decisions related to integrating our two physician services organizations post-close.

·                  Our guiding principles are to create an organization that:

a.              Enables Evidenced-Based Standardized Care,

b.              Promotes Clinical and Operational Excellence,

c.               Creates Innovative Clinical Integration, and

d.              Delivers the Best Sole Source Solution for Customers.

Historically, EmCare and Sheridan have each placed emphasis on these areas. In the future, we will take the strengths from each organization to build a stronger combined organization with a shared set of values and objectives that ensure we are guided by these principles.

Upon completion of the merger, we will be a highly diversified physician services enterprise, with a national footprint and experience in over 25 physician specialties.  Such scope offers us a unique

position in delivering innovation across a broad continuum of care.  At the same time, we must be committed to maintaining a culture that fosters innovation at the local level and creates strong alignment among our providers across all our specialties.  EmCare and Sheridan’s shared presence in certain existing markets will also offer us a unique opportunity to develop our cultural model and clinical collaboration at the local level.

As a start, the steering committee is collaborating on three major work streams that ensure we build a physician services organization with a shared vision, delivery model and culture:

1)             Brand Study: Evaluate the internal and external brand equity and perception of each organization as well as the needs of the healthcare marketplace, which will inform a future-state brand strategy that best positions us as a preferred partner for healthcare clients, enables expansion of client relationships across specialties and establishes us as an employer of choice with core values that resonate with providers.

2)             Organizational Design & Alignment of Specialties: Assess how each organization is operationally and clinically structured and design an enhanced model that will deliver best-in-class solutions within specialties while also driving value creation from integration among our most adjacent specialties.   We will also look to incorporate structures and clinical forums that bring our providers together across specialties within some of our largest markets in order to encourage sharing of market-specific knowledge and relationships.

In order to design the new collective model, it is important to understand the way our respective organizations work today so we can align as fast as possible post-close and swiftly operate effectively as one. To help us in this effort, we created a short survey that will be sent out to provider leadership to garner input. We are personally asking recipients to complete the survey to ensure we have an accurate view of our current organizations.

3)             Support & Service: Assessing how we best integrate our existing physician support centers to insure our leadership has the resources they need to support our major markets, while also driving standardization and efficiency of those support services. Both Project Horizon at EmCare and the RSC project at Sheridan include work streams focused on realigning support services. The work done by those teams will be merged and refined to inform the solution that serves the combined organization’s needs. We believe this initiative will be worth the effort to deliver a unified solution.

As we make further progress, we will provide additional details regarding integration planning and the output from these work streams — including naming clinical and operational leaders who will lead the physician services organization.

What an exciting time to be in healthcare and to be part of an organization with the leadership, resources and expertise to transform the care we provide.

Thank you for all you do,

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If you have any questions regarding the integration of Envision Healthcare and AMSURG or Sheridan and EmCare, please send an email to EnvisionQuestions@evhc.net.

No Offer or Solicitation / Additional Information and Where to Find It

This communication is for informational purposes only and does not constitute an offer to sell or the solicitation of an offer to buy any securities or a solicitation of any vote or approval with respect to the proposed business combination between Envision Healthcare Holdings, Inc. (“Envision”) and AmSurg Corp. (“AMSURG”) or otherwise, nor shall there be any sale, issuance or transfer of securities in any jurisdiction in contravention of applicable law. No offer of securities shall be made except by means of a prospectus meeting the requirements of Section 10 of the Securities Act of 1933, as amended. The proposed business combination between Envision and AMSURG will be submitted to their respective shareholders for consideration. AMSURG has caused its newly formed, wholly owned subsidiary, New Amethyst Corp. (“New Amethyst”), to file with the Securities and Exchange Commission (the “SEC”) a Registration Statement on Form S-4 (File No. 333-212885) that constitutes a prospectus of New Amethyst and a preliminary joint proxy statement of Envision and AMSURG. These materials are not yet final and will be amended. After such time that the Registration Statement on form S-4 has been declared effective by the SEC, Envision and AMSURG will deliver the joint proxy statement/prospectus to their respective shareholders as required by applicable law. This communication is not a substitute for any prospectus, proxy statement or any other document that may be filed with the SEC in connection with the proposed business combination. Investors and shareholders are urged to read carefully and in their entirety the preliminary joint proxy statement/prospectus and any other relevant documents that are filed with the SEC when they become available because they contain important information about the proposed business combination and related matters. Investors and shareholders may obtain free copies of the preliminary joint proxy statement/prospectus and other documents containing important information about Envision, AMSURG and New Amethyst, once such documents are filed with the SEC, through the website maintained by the SEC at www.sec.gov. Envision and AMSURG make available free of charge at www.evhc.net and www.amsurg.com, respectively (in the “Investors” section), copies of materials they file with, or furnish to, the SEC.

Participants in the Merger Solicitation

Envision, AMSURG and certain of their respective directors, executive officers and other members of management and employees may be deemed to be participants in the solicitation of proxies from the stockholders of Envision and shareholders of AMSURG in connection with the proposed business combination. Information about the directors and executive officers of Envision is set forth in its proxy statement for its 2016 annual meeting of stockholders filed with the SEC on March 23, 2016. Information about the directors and executive officers of AMSURG is set forth in its proxy statement for its 2016 annual meeting of shareholders filed with the SEC on April 22, 2016 and its Annual Report on Form 10-K for the year ended December 31, 2015 filed with the SEC on February 25, 2016. These documents can be obtained free of charge from the sources indicated above. Other information regarding those persons who are, under the rules of the SEC, participants in the proxy solicitation and a description of their direct and indirect interests, by security holdings or otherwise, are included in the

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preliminary joint proxy statement/prospectus, and more complete information will be available in the definitive joint proxy statement/final prospectus.

Forward-Looking Statements

Certain statements and information in this communication may be deemed to be “forward-looking statements” within the meaning of the Federal Private Securities Litigation Reform Act of 1995. Forward-looking statements may include, but are not limited to, statements relating to Envision’s and AMSURG’s objectives, plans and strategies, and all statements (other than statements of historical facts) that address activities, events or developments that Envision and AMSURG intend, expect, project, believe or anticipate will or may occur in the future. These statements are often characterized by terminology such as “believe,” “hope,” “may,” “anticipate,” “should,” “intend,” “plan,” “will,” “expect,” “estimate,” “project,” “positioned,” “strategy” and similar expressions, and are based on assumptions and assessments made by Envision’s and AMSURG’s management in light of their experience and their perception of historical trends, current conditions, expected future developments, and other factors they believe to be appropriate. Any forward-looking statements in this communication are made as of the date hereof, and Envision and AMSURG undertake no duty to update or revise any such statements, whether as a result of new information, future events or otherwise. Forward-looking statements are not guarantees of future performance. Whether actual results will conform to expectations and predictions is subject to known and unknown risks and uncertainties, including: (i) risks and uncertainties discussed in the reports that Envision and AMSURG have filed with the SEC; (ii) general economic, market, or business conditions; (iii) risks associated with the ability to consummate the business combination between Envision and AMSURG and the timing of the closing of the business combination; (iv) the ability to successfully integrate Envision’s and AMSURG’s operations and employees; (v) the ability to realize anticipated benefits and synergies of the business combination; (vi) the potential impact of announcement of the business combination or consummation of the transaction on relationships, including with employees, customers and competitors; and (vii) other circumstances beyond Envision’s and AMSURG’s control. Refer to the section entitled “Risk Factors” in Envision’s and AMSURG’s annual and quarterly reports for a discussion of important factors that could cause actual results, developments and business decisions to differ materially from forward-looking statements.

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