I agree with Pete. The two most internationally recognised and accepted qualifications are the CELTA and the Trinity Cert TESOL. Most employers do not make a distinction between these two in terms of the qualifications they accept.
There are many other good quality courses available of equivalent length (120 hours) and content, and you'll find that more and more employers are starting to recognise these as suitable alternatives. But, as Pete says, it is always best to check with individual schools, or have a look at some job ads for Italy to get an idea of what schools are typically asking for.
I hope this helps.