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We analyze the quantum consistency of anomalous abelian models and of theireffective field theories, rendered anomaly-free by a Wess-Zumino term, in thecase of multiple abelian symmetries. These models involve the combinedHiggs-Stuckelberg mechanism and predict a pseudoscalar axion-like field thatmixes with the goldstones of the ordinary Higgs sector. We focus our study onthe issue of unitarity of these models both before and after spontaneoussymmetry breaking and detail the set of Ward identities and the organization ofthe loop expansion in the effective theory. The analysis is performed on simplemodels where we show, in general, the emergence of new effective verticesdetermined by certain anomalous interactions.Comment: 67 pages, 26 figures, replaced with revised final version, to appear  on JHE

Stückelberg axions and the effective action of anomalous abelian models 1. A unitarity analysis of the Higgs-axion mixing