  We establish two exact sequences for the lattice cohomology associated with
non-degenerate plumbing graphs. The first is the analogue of the surgery exact
triangle proved by Ozsvath and Szabo for the Heegaard-Floer invariant HF^+; for
the lattice cohomology over Z_2-coefficients it was proved by J. Greene. Here
we prove it over the integers, and we supplement it by some additional
properties valid for negative definite graphs. The second exact sequence is an
adapted version which does not mix the classes of the characteristic elements
(spin^c-structures); it was partially motivated by the surgery formula for the
Seiberg-Witten invariant obtained by Braun and the author. For this we define
the `relative lattice cohomology' and we also determine its Euler
characteristic in terms of Seiberg-Witten invariants.
