Transits/Flight connections or Visiting other Schengen countries  for a short stay when:

A. Waiting for the first issue (with a valid entry Visa):

• you are allowed to make flight connections or transit in the Schengen area provided that the entry visa (type D) is still valid.
• you are allowed to travel in the Schengen area for no more than 90 days in any 180 day period (the 180-day period considered always runs prior to the control date) provided that the entry visa (type D) is still valid. See the EU calculator tool. 
  Once in the country you may be asked to report the presence to the local police.

B. Waiting for the renewal or in case of conversion of the permit: 

• neither transits nor flight connections in the Schengen Area are allowed.
• you are allowed to travel directly from Italy to your country of origin/residence with the post office receipt by crossing different national borders (for example you can fly from Rome and enter Italy in Milan). Make sure to have with you the expiring permit of stay and the post office receipt.  

C. Holding a valid residence permit

• you are allowed to make transit/flight connections or travel to any Schengen country and stay there for short visits no more than 90 days in any 180 day period (the 180-day period considered always runs prior to the control date. See the EU calculator tool) with the residence permit and the passport. Once in the country you may be asked to report the presence to the local police.