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For a link in a thickened annulus $A \times I$, we define a $\mathbb{Z}\oplus \mathbb{Z} \oplus \mathbb{Z}$ filtration on Sarkar-Seed-Szab\'o'sperturbation of the geometric spectral sequence. The filtered chain homotopytype is an invariant of the isotopy class of the annular link. From this, wedefine a two-dimensional family of annular link invariants and study theirbehavior under cobordisms. In the case of annular links obtained from braidclosures, we obtain a necessary condition for braid quasipositivity and asufficient condition for right-veeringness, as well as Bennequin-typeinequalities.

Annular link invariants from the Sarkar-Seed-Szab\'o spectral sequence