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Pretty much every time Akari meets Cait Sith. Especially notable to this troper is episode 21 of Aria the Natural when Cait Sith invites Akari on some special train and she gives away her ticket to a kitten. He holds her face so intimately and she looks so happy to have her cheeks rubbed with his giant paws...it might seem ridiculous but this troper got all fuzzy inside.
"May this town's kindness reach the hearts of many people..."
A small one in episode 5 of Season 1: The girls are at a beach and Alice discovers a small outcropping above the water. Even after Aika and Akira run past her and jump right in, she's still nervous about the height. Akari soon catches up and is also afraid of the height, but she takes Alice's hand and they jump in together.
"Self-imposed Rule #5: Athena-senpai isn't just anyone, so she's allowed to help at any time."
At their final meeting, Cait Sith promises to Akari that he'll always watch over her even if they can't directly meet anymore. Fast forward to the final chapter and learn he's doing just that.