I am an American trying to get dual citizenship in

I am an American trying to get dual citizenship in Italy. My father’s name when he was born is Antonino. In the US he used Anthony. That is my first problem. 
My second problem is my father’s birth certificate. On his birth certificate from 1903, his date of birth is listed as 6/22/1903. In the US he used 6/19/1903. Since my father is deceased, I don’t know why he did this. I was told that since he was born in his house and delivered by a midwife, the birth was probably registered 3 days later and that is why they used that date. 
Since everything has to match exactly when applying for dual citizenship, I need to know how I can remedy this. Any suggestions?