As far as I know, you generally have to take the IMAT to transfer into Italian medical schools. There are a few exceptions, but for the vast majority, you should have to sit the IMAT like you're trying to get into year 1. Then afterwards, you have to rank along with everyone else. Since you're non-EU, you will be ranked with other non-EU students. If you rank high enough to get into your chosen universities, then you can ask for recognition of courses you have completed in your previous medical school. The problem is that you will usually not know whether or not you will be allowed to join another year besides year 1, until you have completed the IMAT and been admitted into the medical school, because only then will the various departments look at your transcripts and determine whether or not they closely match their own syllabus. Depending on the school, you may be allowed into the 2nd year or any other year, as long as your transcript matches closely to their syllabus (usually the 5th and 6th years are nearly impossible to tranfer into, from non-Italian medical schools); you may be allowed into the 2nd year with the agreement that you have to sit and pass some exams that do not appear to have been completed in your previous medical school; you may not be allowed to progress to an upper year because your transcripts do not match their syllabus close enough, in which case you would be asked to start from year 1. So before choosing your medical schools, try and look up their syllabi online, and compare it to your university transcripts; even then, there might be courses that are similar to what you have done, but some medical schools may still not accept it. It's just bureaucracy.
Alternatively, you can try to transfer without ranking by the IMAT. This usually happens around october/November, when the medical school has already taken in all their students, both new and transfer for the semester. The problem here is, there are not likely to be any places left for any transfers at the time of the year, which is why the IMAT is the most logical route to follow, if you actually intend to transfer.
And just as a side note, medical school is not free in Italy; it can be really cheap depending on your particular situation, as cheap as 500 euros per year for some students, but its not free.