Well, what your animation shows is someone riffling pages as one other answer states.
But an alternative understanding relates to the older flip book technique (see https://en.wikipedia.org/wiki/Flip_book) that animated *.gif files digitally reprise/simulate.
So, you have choices, 'flip' or 'riffle' through. I prefer 'riffle through' as it implies going ...
I would describe the action in the gif as riffling.
Riffle - gerund or present participle: riffling
turn over something, especially the pages of a book, quickly and casually.
"he riffled through the pages"
This implies a casual action, if you want a similar process but implied urgency then you could use the similarly spelled rifling
Rifle - ...
Like taking cream off milk. Cream of the crop.
Very casually. Sort of annulling the very incentivizing purpose.
And cycling. Cycled.
As if it was a hanging calendar or scoreboard that resets when over-used.
I suspect your question will be closed as it leans to asking what to write (I'm not completely sure though, so no close vote from me yet), but I'll give you some of my ideas anyway.
The GIF shows the reader not really comprehending what the book is saying (unless they are incredibly fast at reading), rather they are jumping across pages, perhaps to find a ...