Hi,
There must be some issue with the code you have written.
I have already made a code ready that works and even the last item of the third list (Scegli una sezione) when clicked does show up the list below "Scegli una categoria".
[EDIT] Infact, I have developed the code and its almost ready, will not take more than a few hours to sure your needs. I would have loved to show you screenshot but, not sure how to attach a file here!
Regards,
Sudipto