  There are a number of homological knot invariants, each satisfying an
unoriented skein exact sequence, which can be realized as the limit page of a
spectral sequence starting at a version of the Khovanov chain complex.
Compositions of elementary 1-handle movie moves induce a morphism of spectral
sequences. These morphisms remain unexploited in the literature, perhaps
because there is still an open question concerning the naturality of maps
induced by general movies.
  In this paper we focus on the spectral sequences due to Kronheimer-Mrowka
from Khovanov homology to instanton knot Floer homology, and on that due to
Ozsv\'ath-Szab\'o to the Heegaard-Floer homology of the branched double cover.
For example, we use the 1-handle morphisms to give new information about the
filtrations on the instanton knot Floer homology of the (4,5) torus knot,
determining these up to an ambiguity in a pair of degrees; to determine the
Ozsv\'ath-Szab\'o spectral sequence for an infinite class of prime knots; and
to show that higher differentials of both the Kronheimer-Mrowka and the
Ozsv\'ath-Szab\'o spectral sequences necessarily lower the delta grading for
all pretzel knots.
