Muon accelerator beams are commonly produced indirectly through pion decay by interaction of a charged particle beam with a target. Efficient muon capture requires the muons to be first phase-rotated by rf cavities into a train of 21 bunches with much reduced energy spread. Since luminosity is proportional to the square of the number of muons per bunch, it is crucial for a Muon Collider to use relatively few bunches with many muons per bunch. In this paper we will describe a bunch merging

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... that should achieve this goal. We present for the first time a complete end-to-end simulation of a 6D bunch merger for a Muon Collider. The 21 bunches arising from the phase-rotator, after some initial cooling, are merged in longitudinal phase space into 7 bunches, which then go through 7 paths with different lengths and reach at the final collecting "funnel" at the same time. The final single bunch has a transverse and a longitudinal emittance that matches well with the subsequent 6D rectilinear cooling scheme.