  In the context of discrete Morse theory, we introduce Morse frames, which are
maps that associate a set of critical simplexes to all simplexes. The main
example of Morse frames are the Morse references. In particular, these Morse
references allow computing Morse complexes, an important tool for homology. We
highlight the link between Morse references and gradient flows. We also propose
a novel presentation of the Annotation algorithm for persistent cohomology, as
a variant of a Morse frame. Finally, we propose another construction, that
takes advantage of the Morse reference for computing the Betti numbers in mod 2
arithmetic.
