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AMP as PWA vs AMP in PWA

There are 3 ways to combine AMP with PWA (as described here):

1. AMP pages with PWA features
2. AMP as entry point into your PWA
3. AMP as data source for your PWA

In both first and third approach, we are fetching AMP content from the server using service worker, modify it if required and render. Can someone please explain the difference between these approaches? What exactly is the use of 'Shadow AMP' API?