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Milan produced one of the longest sprints of the season in Andora, where he was overtaken by Christophe Laporte (Visma-Lease a Bike) before powering back to the front and ahead of a fast-finishing Groves (Alpecin-Deceuninck) and Phil Bauhaus (Bahrain Victorious).
The Lidl-Trek rider cut an emotional figure after the race, having doubled his personal tally of stage wins at the Italian Grand Tour.
“I have so many emotions now,” Milan said. “I said from the beginning we came here with one goal for everyone so today the guys did an amazing job and it was such an amazing sensation to win here again at the Giro d’Italia.
“I really have to say thanks always to my teammates. First, they believed in this day, and also, it’s special because my parents were here, so I’m really happy about it.”
It was something of an Italian reunion during the stage, with Filippo Ganna (Ineos Grenadiers) launching a signal of intent and attacking roughly three kilometres from the finish line.
Ganna’s move ignited the chasing pack to increase their tempo on the final downhill portion of the 190-kilometre stage, where they soon neutralised his threat in favour of a bunch sprint.
Groves and fellow Australian Caleb Ewan (Jayco-AlUla) were among those in contention, but it was Milan who finished the fastest off the back of an impressive lead out from compatriot Simone Consonni.
“We saw Ganna going really full gas in the last climb, we caught him (with) 900 metres to go,” Milan explained.
“He also helped us in a way, let’s say, and then Simo did just a fantastic lead out, and I just had to play my cards.”
The nature of the stage meant the general classification remained unchanged through four days, with Tadej Pogacar (UAE Team Emirates) safe in the pink jersey.