Thi surname is typical of Northern Italy, especially Emilia-Romagna region (Bologna region), Lombardy (Milan region), Veneto (Venice region). It comes mostly from name of places: Like for instance "Zerbo". In Venice area this surname or the original variant "Zerbi" coul d come from a dialect word "zerbo" that means "not ripe" or "green". In Sicily the surname "Zerbi" could come from a dialect greek word "zerbos" that means left-handed.
I ignore if this surname could be of slavic origin.
Variants of Zerbi: Zerbo, Zerbio, De Zerbi, Del Zerbo, Zerbetto, Zerbetti, Zerbini, Zerboni, Zerbone, Zerbino, Zerbin (venetian form), Zerbinato (venetian form), Zerbinati and so on.
See Emidio De Felice /Dizionario dei Cognomi Italiani (Dictionary o italian surnames)