How to explain relativistic mass with 2 moving systems, but not 3?

Question

All the visual explanations I know work in some kind of "If you are moving relative to something A, while inside A something is moving, the stuff in A has to move slower due time dilation and therefore the mass has to increase so the impact(and momentum) stays the same."

Since all moving objects and not only the ones inside of moving objects have their mass increased I have big trouble understanding why these kind of pictures should lead to any understanding.

Could I argue that if A was moving his whole point-of-view would be moving?
As if everything already would be inside of something moving?
This sounds very wrong and just raises more questions in my head.
You could simply determine who was moving if that would be true, so it isn't.
Or is it?

I don't know where my thoughts got messed up. Hopefully you do.

Answer 1

If you describe it in such a vague way, it's going to be confusing of course.

There are two reference frames, say A and B. The reference frames are moving with respect to each other. The same phenomon X is described from the point of view of each reference frame. X might be a rocket travelling from some point to another. Clearly, X is a moving object. The only reference frame in which X would not be moving, would be a reference frame that is comoving with X.

Relativity says that some aspects of phenomenon X will be frame-dependent, like the speed of X. While others, will not be. For instance the rest mass of X is an invariant.