At the top of my animation https://www.geogebra.org/m/mjnqb8vk

There are two equal masses moving inertially towards each other until the
inelastic collision.

The moment the two bodies collide, two forces are activated that act
almost instantaneously and then disappear.

They are the blue force with which the first mass accelerates the second
from 0 to v/2 and the red force with which the second mass brakes the
first from v to v/2.

Are they both forces by which the inertia of one mass is activated against
the inertia of the other and vice versa?

Luigi Fortunati

[[Mod. note -- In physics we never say that inertia is "activated".
Rather, we say that all bodies (of nonzero mass) have inertia at all
times. For any body X (of nonzero mass), to accelerate X requires
(implies) that there be a net force F_net(X) acting on X.

In your animation the red arrow shows F_net(the right body), while
the blue arrow shows F_net(the left body).
-- jt]]