  We consider Schr\"odinger operators with dynamically defined potentials
arising from continuous sampling along orbits of strictly ergodic
transformations. The Gap Labeling Theorem states that the possible gaps in the
spectrum can be canonically labelled by an at most countable set defined purely
in terms of the dynamics. Which labels actually appear depends on the choice of
the sampling function; the missing labels are said to correspond to collapsed
gaps. Here we show that for any collapsed gap, the sampling function may be
continuously deformed so that the gap immediately opens. As a corollary, we
conclude that for generic sampling functions, all gaps are open. The proof is
based on the analysis of continuous $SL(2,R)$ cocycles, for which we obtain
dynamical results of independent interest.
