This is more of a "meh" kind of ship for me. I mean, I only ship them as friends pretty much. They are considered to be close friends.
It started out bad and awkward when Peridot made fun of Amethyst in Too Far. But Peridot was able to push Amethyst out of the way of the drill when it was accidentally turned on. In hit The Diamond, Amethyst would rather willingly ambush the other Rubies to protect Peridot. So, they do care for each other that they would protect each other. In Beta, Peridot convinces Amethyst to not fight Jasper alone, knowing that she would poof or get shattered.
In the beginning of the same episode Peridot was excited to see Amethyst, ignoring the fact that Steven is there too.
So, basically it's more of a close friend-shipping than romantically shipping Amedot.
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My Thoughts and Opinions on Steven Universe Ships
FanfictionRead the title. This will contain my many thoughts and opinions on ships in Steven Universe.