  We show that on a dense open set of analytic one-frequency complex valued
cocycles in arbitrary dimension Oseledets filtration is either dominated or
trivial. The underlying mechanism is different from that of the Bochi-Viana
Theorem for continuous cocycles, which links non-domination with discontinuity
of the Lyapunov exponent. Indeed, in our setting the Lyapunov exponents are
shown to depend continuously on the cocycle, even if the initial irrational
frequency is allowed to vary. On the other hand, this last property provides a
good control of the periodic approximations of a cocycle, allowing us to show
that domination can be characterized, in the presence of a gap in the Lyapunov
spectrum, by additional regularity of the dependence of sums of Lyapunov
exponents.
