AMP, as pushed by Google, is essentially Google re-hosting a pared-down, mobile-friendly version of your site.
Alex Kras has two blog posts that got a lot of traction early on that highlighted some issues with this trend [1] [2].
[1] https://www.alexkras.com/google-may-be-stealing-your-mobile-...
[2] https://www.alexkras.com/please-make-google-amp-optional/