By the way,
i don't know if what i've done is correct and can be a usefull "trick", or
it's a rookie mistake, or a casuality. I hope someone knows why this
happens, and could help anyone.

This is:

After trying the "v.patch, v.clean(break,rmdupl), v.build" thing, it was the
moment to create a new column for all geometries, in order to run
v.dissolve.
Then, v.dissolve doesn't worked. I see that v.info gives different
information (number of boundaries, areas, islands...) of the "same" map,
obtained from v.overlay's or v.patch,v.clean... 

Then, I've tryed this:
   v.patch input=quad1,quad2,quad3.............quadN output=quadS
   v.overlay ainput=quadS binput=quadS operation=or output=MAP

And then, I've obtained the same map that running
   v.overlay quad1 or quad2 -> sum
   v.overlay quad3 or sum -> sum
   ....
   v.overlay quadN or sum -> MAP
 
but MUCH MORE FASTER, obviously.

After that, I passed that MAP to create the common column and running
v.dissolve, getting the right result.
-- 
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