A natural, and popular, way to approach the identity of a continuant under a sortal F is to suppose there to be:
(a) A synchronic F-unity relation, binding bits of a world-slice into discrete F-stages.
(b) A diachronic F-unity relation, binding series of F-stages into F's.
In a Minkowskian world, of course, the synchronic and diachronic relations must reveal themselves as simply aspects of a single unity relation for F. But since the proper time of the continuant itself is the most natural generator of space and time axes, the decomposition of the unity-relation into (a) and (b) will normally be effortless.