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We introduce deformations of lattice cohomology corresponding to the knothomologies found by Ozsv\' ath, Stipsicz and Szab\' o in \cite{OSS4}. By meansof holomorphic triangles counting, we prove equivalence with the analytictheory for a wide class of knots. This yields combinatorial formulae for theupsilon invariant.

Deformations of lattice cohomology and the upsilon invariant