general relativity - Causal and Global structure of Penrose Diagrams

What kind of global and causal structures does a Penrose diagram reveal?

How do I see (using a Penrose diagram) that two different spacetimes have a similar global and causal structure?

Also,

I have the following metric

$$ds^2 ~=~ Tdv^2 + 2dTdv,$$

defined for

$$(v,T)~\in~ S^1\times \mathbb{R},$$

e.g. $v$ is periodic.

This is the according Penrose diagram:

Is the Penrose diagram that I have drawn correct?