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The game started in a lively fashion, with both sides creating threatening chances from the first whistle. Napoli's Allan teased in an inviting cross but none of his teammates could make contact with the ball.
Gaetano Letizia replicated Allan's effort and produced a similar outcome as both sides came close to breaking the deadlock.
The best chance of the first half fell to Marek Hamsik, as the attacking midfielder was left wide open with a free header, but the Slovakian forward could only aim it right at Francesco Benussi in the Carpi net.
The match cooled down after the restart, as both sides looked to get themselves back into the rhythm in which they ended the first half.
Despite the lack of second-half chances, Napoli did have the ball in the back of the net but it was correctly ruled out for offside, as Jose Callejon headed in from a cross but the winger made his run too soon.
The result means that Carpi pick up their second point of the season but it still leaves them 19th in the table without a win under their belt.
The goalless draw also leaves Napoli in 11th.