Karkat always had a flushed crush on Nepeta. He never told anyone, as if it should be a secret as dark as his blood color. He was never quite sure if she felt the same way, and everyone though that he was madly flushed for Terezi, so he kept it a secret, going with what everyone else thought.
The time on the meteor really help Karkat with his feelings for Nepeta. After some time stuck on it, Karkat and Nepeta shared their feelings. It was a really sweet moment between the two in a hallway that was empty, with the exception of those two in it. They were overjoyed with the fact that they could be matesprits, and they did fill each other's flushed quadrant.
They each told their moirails about their new relationship, and at least Gamzee was completely on board with it. Equius was a little nervous about it, not anything happening to his moirail. After a few days and seeing how sweetly Karkat treated Nepeta, Equius lost his fear of harm from Karkat and was fine with the relationship.
They spent most of their time together, mostly in Nepeta's room with her ships. Sometimes, they had to be forced out of the room to have something to eat. They hardly left each other's side, extremely happy together. When the two were alone, Karkat wouldn't yell for her, but Nepeta was fine if he yelled.
The incident with Gamzee was terrible. Karkat knew that a moirail always comes before a matesprit, but he couldn't help but worry about Nepeta. After he shooshed Gamzee to highness, Karkat tried to find out what happened to Nepeta. She wasn't on the roof with them, and it worried him.
When he found the blood that Gamzee didn't take for his potions, Karkat was devastated. He locked himself away from everyone. When he did sleep, he tried to look for his Nepeta in the dream bubbles, but he never found her.
Soon, Karkat forgot about Nepeta, but one day, when he was really bored, he happened to talk into her old room. He stares at the ships again, finding her OTP quite quickly. He walks over to it, finding their handprints by it easily. He broke down in tears, his old memories and feelings coming back to him.
For many days after that, Karkat stayed in that room as much as he could. Dave was of course worried about him, and helped get through it. Whenever Dave tried to get him to go back to his own room, Karkat shout more than usually. Dave decided to stay with him, not wanting to leave him alone at all.
One day, Dave had to leave Karkat alone for only a few minutes. Those few minutes changed everything. He came back to find Karkat lying on the ground in front of Nepeta's OTP, candy red liquid surrounding his body. On the OTP itself, in candy red, three words were written: "I love you."
Karkat killed himself to be with Nepeta, his last words I love you. Dave couldn't believe that it wasn't his fault that Karkat committed suicide. Everyone tried to convince Dave, but it was impossible to make him think otherwise.
Karkat though, had woken up in the dream bubbles to find the Nepeta that he lived with and loved nearby. The two quickly picked up on where they left off with their matspritship, and they were happy together in the dream bubbles, no harm coming to them.
I couldn't leave this with a sad ending. This is one of my favorite ships, and I literally cried when I wrote the ending. Sorry for giving you some sadstuck, but I had to come up with a way to show that this is in a doomed timeline, but I really wanted a happy ending, even if it was really quick.