Amane and Canary don't interact much - so far we've seen them together only in the 13th Hunter Chairman Election arc. Their initial dynamic there consists of Amane treating Canary rather coldly and Canary planning to sabotage Amane and Tsubone on Killua's behalf.
Canary’s sabotage was very simple. Canary rode with Amane on Tsubone's motorcycle form to chase after Killua and Alluka when they were running away. After catching them at the airport, Canary distracted Amane by pretending to need help booking a flight, so the siblings can escape.
Failing her duty as a Zoldyck butler caused Amane lose her cool in front of Canary, who commented that the real Amane is cute. Amane blushed assuming Canary was making fun of her, but Canary assured the other girl that the compliment was genuine.
At the end of the arc they were shown mourning Gotoh together. They were both tricked by the Kiriko acting as Gotoh, which caused Amane to reveal her “real side” that Canary thought was cute.
Both girls don't seem to have much in common and so far have been shown as quite big opposites. The only similarities between them we've already seen are them being equally loyal and focused on their duties. They both are also the Zoldyck butlers - because of that part, if the ship was made canon it would have almost a forbidden love dynamic, as Illumi Zoldyck states that butlers cannot have lovers.
Amanary is one of the most popular femslash ships in the Hunter x Hunter fandom. The shippers interpret Canary thinking Amane is cute as a romantic attraction and consider Amane a tsundere, because of the blushing and her general attitude towards Canary.
|SHIPS||het||Killunary • KuroNeo • OuMugi • Ponzukkle|
|Chrollinks • HisoGon • HisoIllu • HisoKuro • Killugon • Leopika • PariGing • PhinFei|
|family||Hisoka x Abaki|