Yes, you can travel to your home country with your ricevuta receipt from the post office, but you cannot travel to other Schengen Areas with a Permesso di Soggiorno receipt.
The first and most obvious benefit of a Permanent Stay Permit is the relief from the yearly gathering of documents and visits to the Questura. Say bye-bye to that!
The Permesso di Soggiorno per Attesa Occupazione also called “Atessa di Lavoro” gives a one-year grace period to new graduates, who are not Europeans, to search for a job.
Expired permesso di soggiorno can be a pain in the butt. It’s time to queue up again and carry on with the endless paperwork.
Permesso di Soggiorno is a paperwork most foreigners dread most in Italy, it is never done. The first frustration is the language, especially if you have no knowledge of Italian.
If you need to travel to another country other than your home (and within the Schengen Area), then you must request the Permesso di Soggiorno Provvisorio.