Thanks to all, in the end I never found the detail with the arduino nano, I think the problem is manufacturing. I tried some changes among those who mentioned me and the problem persisted.
The solution was to change arduino, i try with an arduino one of Steren and the problem was the same, the one that worked was an arduino Chinese one, I could feed it with the battery and it worked without problems, so I guess it was design problem of the other two.
Thanks again everyone for your answers!