  We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened
annulus, A x I, has the structure of a bifiltered complex whose filtered chain
homotopy type is an invariant of the isotopy class of L in A x I. Using ideas
of Ozsvath-Stipsicz-Szabo as reinterpreted by Livingston, we use this structure
to define a family of annular Rasmussen invariants that yield information about
annular and non-annular cobordisms. Focusing on the special case of annular
links obtained as braid closures, we use the behavior of the annular Rasmussen
invariants to obtain a necessary condition for braid quasipositivity and a
sufficient condition for right-veeringness.
