I am sorry, but I must offer a different viewpoint. As a United States vessel you are required to check out of Italy and turn in your Transito. This is definitely true if you do not plan to return to Italy.
Now I will say that when we left Italy to go to Malta for a two-week trip I did not check out of Italy. I did check into Malta, at Gozo. And then when I left Malta to come back to Italy I only informed them by radio
We returned to our birth in Marina de Ragusa without informing the authorities that we had ever left the country.
Vessels registered in the EUdo not have to jump through these hoops, but as a US vessel you do.