Stability, unstability (and metastability) in liquid-gas phase transition: unstable in regards to what?

I have a question about the stability, unstability (and extra questin about metastability, between the spinodal lines if you have time), when we are having a liquid gas phase transition.

Here, a curve including the spinodal lines. The main thing to look at is in fact the red line obtained by Maxwell construction.

My question is mainly: What do we precisely mean by “unstability” in the phase transition, and how will the system move when I prepare the system in given states.

The volumes $V=a$ and $V=b$ represent the spinodal lines. Between those two curves the system is said unstable.

Between $V_1$ and $a$, $b$ and $V_2$, the state is metastable.

But I want to make things really clear: what do we precisely mean by “stable” and “unstable” zones of the diagram?

Does it mean that if I take an initial state such that:

• the temperature corresponds to this curve $P(V)$ (because it is isothermal curves here)

• the volume is such that $a leq Vleq b$

And then from this initial state, I fix $(T,P)$ and I let the volume change.

The system will be unstable in this $(T,P)$ ensemble (the volume will change until reaching the equilibrium). And in practice this zone also corresponds to the phase transition liquid-gas. Thus when the talk about stability, unstability here, they implicitly assume we are in $(T,P)$.

Am I right?

I advise to take a look at the beginning of page 64 of this document for further info if you want a more detailed context https://www.uam.es/personal_pdi/ciencias/evelasco/master/tema_III.pdf

Extra question: If I am right with my previous explanation, what happens if I initialize my system in the metastable zone : $V_1 leq V leq a$? How do I know if the system stays here, go to do a phase transition to reach the stable state in the “other direction”, go to the stable state just at $V=V_1$?