Easiest:
Use the array exclusion filter in p2.
In p3 display by subquestion relevance.

Joffm 

thanks for your response. Could you give me an example or a link to take as a reference and do the tests?

Well, LS is doing in p3 exactly what you are asking it to do, at least in the first LSS file that you have provided. 


In p3 you used the array exclusion filter based on p1 and p2. So what does LS do? It hides in p3 thos answers, that have been chosen in p1 and p2.Here is the tool tip that explains what the "array exclusion filter" does:

What you want is the "normal" array filter I guess. For the "normal" aray filter it shows only those answers, that have been chosen in the previous questions you base your array filter on.However, I think you will run into trouble with what you are trying to do, because you use two questions with the same question codes (p1 and p2) in your array filter. If you will look a the logic file of p3 if you switch to the normal array filter you will see this: 
 

What happens there? LS checks for p3_1, so the answer "uno" if p2_1 is NOT empty AND p2_2 is also NOT empty. But due to your array filter exclusion used in p2, this must always be untrue. Because in the p2 you always hide the answers that were marked in p1, so they are always empty.So your are blocking yourself with these nested array filters.But, as due to the question type you are using, you do not need to use the array filters, but you can apply relevance equations / conditiosn to each subquestion individually which will allow you to do what you want to do (show and hide subquestions/answer options) based on your idea without having the interfearance of the differen array filters on each other.In p2 you simply check if the answer was chosen in p1 and then you hide the respective subquestion. In p3 you do somehow the opposite. You check if the answer option was chosen in p1 OR p2 and if so, you show it, if not you hide it.