Today I looked at breathing in different animations. I firstly looked at Telepurte's short animation, which shows someone lying down and breathing in a relaxed way.
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In contrast, Caesar Zeppeli's breathing is a lot more panicked and shallow than Telepurte's animation (Episode 20 Battle Tendency, made by David Production and directed by Naokatsu Tsuda).
I learned from these two animations that to show breathing in animation the core/chest expands/contracts, the shoulders raise/lower and the head moves up/down.