Bring a Carpet to the pit

What is it?
You can make upto 3 Carpets in Sunken City follow you down to the end of the level from Rest area.

With proper timing, its possible to have Carpet(s) visible in the History Lesson too.

How and where to do it
Explanation in text is missing! if someone understands the specfics / one method, please add instructions here.

Video in Japanese and japanese subtitles
It contains enough hints, to be able to reproduce it.

Trivia
Carpets have families too, don't forget to lead the carpets back home after the fun is done.