How we migrated our entire site to AMP without the user noticing (AMP Conf '19)

AMP provided us the opportunity of improving the performance of our website. We started adding AMP version for some pages, having both AMP and non-AMP pages running together. Based on results, we decided to keep just the AMP version, which we accomplished gradually without the user noticing the changes. We ended up with an almost 100% AMP site.