The relation with Nao is the most important thing in Akiyama's development.
He restarts to believe in someone thank to her and decides to help a honest girl not just beacuse she reminds his lost mother, but because she's the kind of girl that needs protection and friendship. The world isn't easy to live and Nao is so honest that everyone tries to trick her.

Akiyama is the one who saves her in every circumstances. Their meeting is a sign of destiny and Akiyama knows very well her preciousness, because, nowadays, a girl like her is a rarity. Nao can really teach honesty to the others and Akiyama is by her side. He helps her with all himself, even if the Liar Game is rich of difficulties and risks.

His feelings for her aren't clear but I'm sure that in the bottom of his heart, it can't be a different person. She's the only that, with a gentle word and a sincere smile, could realize Akiyama's resurrection as person and guy! :)

They're not canon but I'm sure that in future their feelings will have the right importance!