I think that throughout all three films Neri has played many roles within the family. He has been a loyal bodyguard to Michael, he took over Tessio's caporegime in #1 and was always a button man. Even in GFIII the family relies on him to light a candle for the archbishop. He is truly a valued and useful member of the family.

As Puzo described in the book Neri was the best thing to happen to the family since Luca Brasi.