Hey @Daniele
I just tried page transitions/pjax and got some initial feedback. I’m not expecting to get a solution anytime soon, if any - but if you might give a response if there could be a easy-fix (since those plugins are basic, popular ones)
- If you switch the website language, the header isn’t translated / language switcher not switched. (At least using Translatepress)
- Woocommerce cart is’t persistand (if you remove an item, switch to another page and click on cart again – it’s back again).
Just some first feedback. I know such issues might occur using pjax & WP. Still love the possibility to create pjax websites 
.