On Special Relativity - Active Frame

It is a question that has stumbled me since long time ago. Perhaps one of those obstacles that discouraged me from pursue of quantum mechanics.

Let there be 2 stars, stationary. Thus, should any star moves toward another, there are 3 possible frames of reference: star A, star B...and the third frame is the story teller's frame (or an outside observer of A & B, perhaps regardless of his location).

It would seem that should any star moves toward another, there will be 1 frame of which its observer will have his detection of the 'crisis' delayed, unless this frame belongs to either the story teller's frame or the frame of the star that initiates the move: In other words, I called it the active frame.

If that is the case, unless I'm missing something, how does it not matter in identifying which star that moves? As to the notion of either star could be the moving ones.

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