I see you have had a lot of answers but just thought I would add my recent experience.
We moved to Bologna at the beginning of March (ahead of a brexit deadline as well!). We took an AirBnb for a month, naively thinking it would be enough time to find somewhere to rent... it wasn't! We found eventually that looking online and sending emails was pointless, noone replies and when I started phoning or visiting most properties we saw advertised had already gone almost instantly (also, as I only had a 6 month contract at the time the agencies weren't interested in talking to us, despite being able to demonstrate available funds and offering several months rent in advance!). We ended up with Airbnbs for the first 6 months in the end. However, we were able to negotiate a short term contract with an Airbnb owner directly after having stayed in their place for a month. With this temporary (tourist) contract we were able to get temporary residency (anagrafica) from the local comune, which I believe is enough to grant the same 'stay of execution' that a residency application will. If I had my time again I would be tempted to find a longer term Airbnb and contact the owner to ask about a contract to buy you some breathing space. We found an apartment and got residency in the end but it was privately through a friend of a friend.