This is the possible former romantic relationship with Kazuha's father,Mr.Migiwa and Akira's mother,Ms.Amatsume.
Yosuga no SoraEdit
Years ago, Mr.Migiwa apparently had an romantic encounter with Ms.Amatsume but broke up with her, lost contact with her and married Kazuha's mother,Mrs.Migiwa. After that, Akira's mother died and Mrs.Migiwa got to hold Akira in her arms while she was an infant so that she would be like a mother-figure to her. Akira claimed to be Mr.Migiwa's illigitamate eldest daughter, however Mr.Migiwa denied having ever known her mother and possibly being her father and disowned her, much to Kazuha's disappiontment. Akira had found a dairy saying that she and Kazuha are "mistaken idenitys and before she could leave on a train, Mrs.Migiwa showed up saying that the DNA results were negative and that Akira and Kazuha aren't half-sisters (though they are half-sisters in the Yosuga no Sora Manga) Due to not being biologically related, Akira and Kazuha persued their love for eachother,kissed and made love, beginning a relationship. It's unknown if Mr.Migiwa and Mrs.Migiwa accept their relationship.