Yevamos, Chapter 4, Mishnah 12. This mishnah presents the dispute over which of the listed forbidden relationships produces a mamzer.
The three cases in the mishnah:
"HaMachazir Gerushaso" - one who remarries the wife he divorced, after she had in the meantime married another man (not merely through relations, but through kiddushin and nisuin). This prohibition is a negative commandment of the Torah, and it carries no kares, only a lav.
"VeHaNosei Chalutzaso" - one who has already performed chalitzah with a woman and now comes to marry her. The prohibition of a brother's wife has already lapsed from her and there is no kares here, yet he may not marry her, as it says, "who did not build his brother's house" - one who did not build his brother's house may no longer marry her. This too is considered a lav.
"VeHaNosei Kerovas Chalutzaso" - one who marries one of the relatives of the woman with whom he performed chalitzah.
In these three cases the mishnah rules: "Yotzi, VeHaValad Mamzer" - he must divorce her, and a child born of such a union is a mamzer. These are "Divrei Rabbi Akiva" - the words of Rabbi Akiva.
Two principles in Rabbi Akiva's approach:
A mamzer results from a plain negative commandment: one who violates a Torah prohibition in forming the marital bond, even where there is no kares, produces a mamzer.
A relative of his chalutzah is forbidden by Torah law: unlike the Sages, who hold that this prohibition is only rabbinic, Rabbi Akiva held that her status is like that of a relative of his divorcee, and she is forbidden by Torah law.
The approach of the Sages:
The Sages disagree and say "Ein HaValad Mamzer" - the child is not a mamzer, in each of the three cases: one who remarries his divorcee, one who marries his chalutzah, and one who marries a relative of his chalutzah.
"UModim BeNosei Kerovas Gerushaso SheHaValad Mamzer":
The Sages nevertheless agree that if a man marries a relative of his divorcee - her mother, her daughter or her sister, that is, a relative of the woman to whom he had previously been married - the child is a mamzer, because all of those relatives carry the penalty of kares. Since that woman from whom he was divorced had been his wife, the prohibitions of her relatives remain in force even after the divorce: the prohibition of a wife's sister does not remain after her death, but after divorce it remains in force; while the prohibition of the mother and the daughter remains whether the former spouse is alive or not.