[voakbasda]

Have you done orienting in the past?

One of the big tricks is to realize that magnetic north (where your compass points) is usually not the same as geographic north (where maps are drawn). The adjustment is local; here, I think magnetic north is 7 degrees off from north.

In the US, the USGS topographic maps contain the required adjustment for the covered area. Not sure about Italy.

[integralid]

I don't think that's it. For me sometimes my phone compass is (roughly) right, but sometimes points in a completely wrong direction, for example 90 degrees off. It calibrates after a while when I start walking but I guess this is what OP had in mind, not a few degree difference.

[jiggawatts]

iPhones can regain the compass fix if you move the phone along a figure eight path while holding it flat and level. Worked pretty well for me in the past.