Grant that there is a self: what makes it the same self over time? Ancient soul theories locate persistence in an enduring substance; empiricist accounts in memory and psychological continuity; phenomenological accounts in the lived continuity of an embodied point of view. Each picks out a different thread as the one that must hold for a person to persist through change.
This is distinct from whether an enduring self exists at all — a prior question the map treats separately under Existence of the Self.