Canzi started his coaching career in 1985, working as a youth coach for a variety of amateur clubs.[2] During these years, he also graduated in sports science in 1994 and did several small jobs, including working as an entertainer and an ambulance volunteer.[3]
In 2001, Canzi took on his first head coaching job at Eccellenza amateur club Sandonatese; in 2005, he moved to Promozione club Paullese.[4] In 2007, he met Mario Beretta and joined his coaching staff at Siena, then following him at his later managerial roles at Lecce, Torino, Brescia, Cesena, Latina and PAOK FC.[4]
In 2015, Canzi accepted a new role as the Under-19 coach of Cagliari.[5] After five years at Cagliari, in 2020 he took his first head coaching job in a professional team, taking over at fellow Sardinian club Olbia in the Serie C league, a role he filled in for two seasons before departing in May 2022.[6] He then briefly worked at fellow Serie C club Turris during the pre-season, being sacked just a week before the first matchday of the regular season.[7] In October 2022, Canzi returned to management as the new head coach of Serie C club Pontedera.[8]
After two positive seasons at Pontedera, on 10 May 2024, Canzi announced his departure from the club.[9] On 22 May 2024, he was unveiled as the new head coach of Juventus Women.[10]