Simple Paginated Popover

Can "popover" UIs be paginated, or should they show a fixed set of content? Here's an animated wireframe I made to try to figure it out.

Confessional: I spent most of my time on the motion of the circular buttons in the tab bar at the bottom, trying to make sure they responded enough to be intuitive, without being to cartoonish.

HMU if you have feedback.