Persians consider Gilani and Mazandarani as Persians. They are a sub-division within Persians similar to Lurs, Bakhtiarys etc.

This is what Azeri Turks say about Gilani and Mazandarani:

"The Mazandarani and Gilaki groups fall inside a major cluster consisting of populations from the Caucasus and West Asia and are particularly close to the South Caucasus groups—Georgians, Armenians, and Azerbaijanians"

In other words, they claim Mazandarani and Gilani as subgroups of Azeri Turks.