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We show that a set of parallel 3-brane probes near a conifold singularity can be mapped onto a configuration of intersecting branes in type IIA string theory. The field theory on the probes can be explicitly derived from this formulation. The intersecting-brane metric for our model is obtained using various dualities and related directly to the conifold metric. The M-theory limit of this model is derived and turns out to be remarkably simple. The global symmetries and counting of moduli are interpreted in the M-theory picture.