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We derive the BRST symmetry, Slavnov-Taylor identities and Nielsen identitiesfor the ABJM theories in ${\cal N}{=}3$ harmonic superspace. Further, the gaugedependence of one-particle irreducible amplitudes in such superconformalChern-Simons theory is shown to be generated by a canonical flow with respectto the extended Slavnov-Taylor identity, induced by the extended BRSTtransformations (including the BRST transformations of the gauge parameters).

Ward identities and gauge flow for M-theory in ${\cal N}{=}3$ superspace