  We present a new method for the determination of the two-terminal
differential conductance through an interacting cluster, where one maps the
interacting cluster into a non-interacting cluster of $M$ independent sites
(where $M$ is the number of cluster states with one particle more or less than
the ground state of the cluster), with different onsite energy and connected to
the leads with renormalized hoppings constants. The onsite energies are
determined from the one-particle (one-hole) excitations of the interacting
cluster and the hopping terms are given by the overlap between the interacting
$N$ particle ground state and the one-particle (one-hole) excitations of the
interacting cluster with $N$-1 ($N$+1) particles. The conductance is obtained
from the solution of a system of $M$+2 coupled linear equations. We apply this
method to the case of the conductance of spinless fermions through an AB$_2$
ring taking into account nearest neighbors interactions. We discuss the effects
of interactions on the zero frequency dipped conductance peak characteristic of
the non-interacting AB$_2$ ring as well as the consequences of a particle
number jump that occurs as the gate potential is varied.
