  We construct deformed, T^2 wrapped, rotating M2-branes on a resolved cone
over Q^{1,1,1} and Q^{1,1,1}/Z_2, as well as on a product of two Eguchi-Hanson
instantons. All worldvolume directions of these supersymmetric and regular
solutions are fibred over the transverse space. These constitute gravity duals
of D=3, N=2 gauge theories. In particular, the deformed M2-brane on a resolved
cone over Q^{1,1,1} and the S^1 wrapped M2-brane on a resolved cone over
Q^{1,1,1}/Z_2 provide explicit realizations of holographic renormalization
group flows in M-theory for which both conformal and Lorentz symmetries are
broken in the IR region and restored in the UV limit. These solutions can be
dualized to supersymmetric type IIB pp-waves, which are rendered non-singular
either by additional flux or a twisted time-like direction.
