San Fran IB ----> NYC PE possible?

Recently received an offer from Centerview Partners in their SF office and am obviously very excited. However, I want to know how common is it for analysts to move to a different city when recruiting for PE after 2/3 years. I am originally from NYC and would want to move back after my analyst years to be closer to my family and don't want to spend my entire career in SF.

P.S: I got into the SF office for Centerview because that was where my entire school's alumni network is and the people I talked to do recruiting for that office. I also asked them if its possible to move me to NYC office and they said no.