Mathematical performance theory  uses a model of performative unfolding that is based on "sexual propagation" of successive performance refinements. It is formally described by a tree-shaped diagram, the performance stemma, starting at the primary "mother" performance that ramifies to a series of "daughter" performances. This propagation mechanism is induced by a series of performance operators stemming from the composition's music analysis. In this paper we refine such networks to performance hypergestures whose curves represent continuous transitions from mother to daughter performances. This level of description uses the theory of Lie-type performance operators and enables a detailed analysis of different performative transition strategies. We then calculate the singular performance hypergesture homology H1 and discuss its significance for the classification of transitional strategies.