  We construct supergravity solutions describing a stack of D3-branes localized
at a point on a blown-up cycle of a resolved L^{a,b,c} cone. The geometry flows
from AdS_5 x L^{a,b,c} to AdS_5 x S^5/Z_k. The corresponding quiver gauge
theory undergoes an RG flow between two superconformal fixed points, which
leads to semi-infinite chains of flows between the various L^{a,b,c} fixed
points. The general system is described by a triplet of Heun equations which
can each be solved by an expansion with a three-term recursion relation, though
there are closed-form solutions for certain cases. This enables us to read off
the operators which acquire non-zero vacuum expectation values as the quiver
gauge theory flows away from a fixed point.
