I don't know if this is something appropriate for this forum, but I can't access the following slides:
https://mysite.science.uottawa.ca/pjacqmin/summary-manifold-functor-calculus-lecture2.pdf
The lecture was about manifold calculus, and it was given by Pascal Lambrechts in July 2019. I've seen other lectures of the same topic given by the same lecturer, and they helped me understand the proof of the eversion of the sphere.
I would like to have more information from this source. I hope someone was quick enough to grab a copy of the PDF.