Spectral flows and twisted topological theories

We analyze the action of the spectral flows on N = 2 twisted topological theories. We show that they provide a useful mapping between the two twisted topological theories associated to a given N = 2 superconformal theory. This mapping can also be viewed as a topological algebra automorphism. In particular null vectors are mapped into null vectors, considerably simplifying their computation. We give the level 2 results. Finally we discuss the spectral flow mapping in the case of the DDK and KM realizations of the topological algebra.