  In this paper we study the spectral asymmetry of (possibly nonselfadjoint)
elliptic PsiDO's in terms of the difference of zeta functions coming from
different cuttings. Refining previous formulas of Wodzicki in the case of odd
class elliptic PsiDO's, our main results have several consequence concerning
the local independence with respect to the cutting, the regularity at integer
points of eta functions and a geometric expression for the spectral asymmetry
of Dirac operators which, in particular, yields a new spectral interpretation
of the Einstein-Hilbert action in gravity.
