  We consider extended CMV matrices with analytic quasi-periodic Verblunsky
coefficients with Diophantine frequency vector in the perturbatively small
coupling constant regime and prove the analyticity of the tongue boundaries. As
a consequence we establish that, generically, all gaps of the spectrum that are
allowed by the Gap Labelling Theorem are open and hence the spectrum is a
Cantor set. We also prove these results for a related class of almost periodic
Verblunsky coefficients and present an application to suitable quantum walk
models on the integer lattice.
