As far as I understand Server.Transfer method is better than the old Response.Redirect method because its improve server request performance by reducing the number of requests. To me that is good enough and as long as the path parameter is clean you will always retrieve the necessary resources to load the page.
Responsive Design is Google recommended display method because the page URL and HTML stay the same. If your URL stays the same but the HTML changes google will classify this format as Dynamic Serving, whereas if URL and HTML changes Google will treat it as Separate URLs.
Each format has a different approach when it comes to SEO. The way you identify the user-agent is also important for Dynamic Serving, Google Recommends using Vary HTTP. In the case of Separate URLs you need to establish the relationship between the URL-Version-1 and URL-Version-2, here Google recommends using the using the <link> tag, where the Desktop version needs rel=”alternate” and the mobile version needs rel=”canonical” to link Mobile and Desktop URLs.
Please take into account that if you are using m.example.com vs example.com they are essentially different URLs.
Whatever your approach might be the bottom line is that you need the following to be always true:
- Make sure the content and links on the mobile site are similar 90% to
the desktop version.
- It is hightly recommended that the content is the same in both
versions (Remember Google Prefers Responsive Websites where URL and
content stays the same).
- Make sure to have structured markup for both the desktop and mobile
version. Use the robots.txt testing tool to verify that your mobile
version is accessible.
- Expandable content such as Read More will have more weight on mobile.
- Page speed of your mobile site will determine the rankings of your
mobile site and desktop site.
- Google has started to use the mobile version of the web as their
primary search engine index.
I highly recommend you to read what Google have said about going Mobile First
