As the levels of absorption deepen, they become more subtle. Tranquility is a synonym of equanimity. The English translation of the Pali term upekkha does not shed much light. How does one differentiate between tranquility & equanimity? Balance comes up in the comentaries. When effort & concentration and intelligence & faith are balanced, that is equanimity. I find that to be too abstract to be very useful in practice.

Absorptions or jhanas are presented as antidotes for the hindrances but equnimity is not presented as an antidote for any hindrance, see pg. 189 In This Very Life by U Pandita. The clue for me is seclusion from the hindrances which deepens with the progression of absorptions. Equanimity seems to match up with vedana or feeling valences (pleasant, neutral, unpleasant). In dependent co-origination desire/aversion (tanha) follow depending on the feeling valence. Thus noting the feeling valence of an originating object in consciousness enables witnessing without progression to desire or aversion. The power of the hindrances is in the strength & influence of the feeling valence. Clearly seeing feeling valence & associated momentum allows for finer choice, for stopping dependent co-origination.

Tranquility has a horizontal or x axis spatiousness. Equanimity has a vertical or y axis vantage point or perspective. Balance is easier with perspective.

In Heartwood of the Bodhi Tree, Buddhadasa describes 2 methods of stopping dependent co-originations, specifically rebirth, pg. 81. Method 1 is noting the origination of an object in consciousness (phassa) without progression to feeling valence. Method 2 is noting the feeling valence without progression to desire or aversion. Both method require observation without a reaction. Noting without reaction is equanimity.