I think the blood reference is just that K. I'm not certain whether Sumire came back to this world though, or whether K. Which leads me to conclude that their re-connection is real. Was it a one-off, that connection? Did Sumire get through that one time and then nothing more? thinking how surprised he was for it to actually be happening, to be vibrating 'real air' and such. I believe the phone call happened, as Murakami describes K. I also don't believe it was a delusion or a dream. The blood, I think, is meant to be taken as the symbolic blood that is referenced often in the novel. I don't feel this is exactly right, but I feel like I'm getting closer to an interpretation that makes sense. When he looks out, he sees they are under the same moon-similar to the moon in Greece when he almost crossed over as well, and makes a statement that he knows he 'has time' to find her now, because he indeed has spilled some blood, so to speak, and has crossed over to the world she is in.

I think she was explicitly telling him that he needs to go (figuratively) slit a dog's throat of his own, and come find her by crossing over to her himself, as she had done. Then, after some time, it worked, and she contacted him. He had been focused on dreams and dreaming, just as Sumire had just before she disappeared.

found some way to slip over into the other world. In the real world, he might be dead, just dreaming, or vanished. Now that he is sure that he is alive in the other world, he can be with Sumire and enjoy life. When K mentions traces of blood at the end of the story, he's probably looking for the blood of his dead copy. K doesn't like describing himself, that's why when he saw the moon in Greece, he didn't lost anything. The reason why nobody can find her, is because she now resides in the other world. She probably can't differentiate her real self from the image, that's why the moon took her entirely when she was in Greece. Sumire, in her texts, says that she can't differentiate what she knows from what she doesn't. The myu that enjoys sex and playing the piano is probably in the other side. That night she had the accident in Europe, she lost the ability to play the piano and her sexual desire.

Myu described herself as a succesful pianist and somebody who enjoyed sex. It seems like the moon takes to the other side your image, the way you describe yourself. Characters interact with the other side whenever the moon appears. He also mentions that the moon shows him that he is on the same world as Sumire. After reading the book for second time, I think K went to the 'other side'.

Books like sputnik sweetheart