Why batteries in serial don't discharge each other?

A question that I've asked myself for long time about why batteries in series work as they do. I'll try to explain:

If you take two batteries, let's say A and B, and you put A's anode touching the B's cathode (only that, without closing the circuit). It turns out that not only A and B poles don't discharge each other but the resulting device sums the voltages of both batteries.

When I think of it my idea is that A and B poles should get "lost" (they have cancelled) but the poles that remain unconnected still have a different potential so it shoud work at that voltage, not the sum. After all you are connecting a + pole to a - one and it's supposed that one pole has a different charge that goes to the other until they are balanced.

So, why batteries discharge when closing the circuit but not when it's open if poles of different batteries are in touch? Why the charge from one pole doesn't flow to the other? And why the voltages sum?

I'm afraid that the explanation is quite simple but...which is?

Thanks in advance!

NOTE: I edit my own question. As Murphy states, once published I've found there can be a possible explanation here:

Why two connected 1.5 volt battery become 3 volt

I'll see if it tells me what I want. Nevertheless, feel free to give me your own answer.

NOTE 2: Ok, guys, thank you very much for your answers. Finally I think I got it!

The point is in the electrons that cause the potential difference. The accumulation of electrons in one pole makes impossible that the electrons of the other battery enter the possitive pole. They are rejected electrostatically. Allowing it you would have the two poles charged but the battery doesn't work that way.

So, when you close the circuit, both accumulations of electrons sum because one battery would help expelling the other one's charge pushing with it's electrons.

Am I right?