In which episode of the anime did Kuzan and Akainu fight?
The fight is shown in Episode 583, when it was told by Smoker-san in the midst of the Punk Hazard Arc.
According to Smoker, the battle between these two was so ferocious that it literally changed the weather of Punk Hazard Island. Akainu ended up as the winner, but had sympathy enough to spare Aokiji's life in spite of it being meant as a battle to the death. Unfortunately, Aokiji did not escape unscathed. He parted from the battle with a staggering level of scars and with his left leg reduced to a stump. Though crippled, Kuzan used his Devil Fruit powers to generate a replacement limb out of ice.
From Kuzan article on One Piece Wiki
Episode 583 preview on YouTube showing the scene.
The fight has never been shown: it happened in the 2 years gap and at the moment we just know it was on Punk Hazard and that Akainu won after 10 days of fighting (I hope there will be a flashback at some point showing the fight).
This is a video taken from episode 570 in which Jimbei explains the situation. The fact that they fought on Punk Hazard is explained in episode 582.