Everyone is different, so your question has no definite answer. In my two
trips to Italy, I did not experience problems other than the normal problems
for me. I would suggest being concervative with your insulin on the flight
(take slightly less than you would normally)- you don't want to go hypo
during the flight, plus you can't really tell what the heck they are serving
you. There have been articles written describing how to change your insulin
timing as you move east, but I found it worked just to take a little less
than I normally would with meals while on the plane. The bigger problem will
be the amount of carbs you eat once you get to Italy. The food is fantastic.
You pretty much have to go out of your way to get a less than excellent
meal, but they all involve pasta or rice (risotto). Ans the gelato is
incredible, too, especially in Florence. BTW, gelato is not high in fat, so
there is very little slowing of absorption as there is with ice cream. Bring
extra insulin - you'll need it.

when I cross a lot of time

I'm not on insulin yet but I just got back from a 10-day trip to India.
Take a look at my post on Jet-Lag for some of my experience.
It isn't just being in another time zone, it's like a whole other world.
Take two meters (one in carry on and one packed) and plenty of strips.
Testing supplies weren't readily apparent in any of the stores we visited
there so I was glad I had a lot.

Just a tip on a travel BG meter. I carried a "Sidekick" disposable meter in
my carry-on. It's the size of a 35mm film can and worked like a champ the
whole trip. The meter and 50 tests were $30 US (at Walgreens) and well worth
it for the convenience.