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We investigate flux vacua on a variety of one-parameter Calabi-Yaucompactifications, and find many examples that are connected through continuousmonodromy transformations. For these, we undertake a detailed analysis of thetunneling dynamics and find that tunneling trajectories typically graze theconifold point---particular 3-cycles are forced to contract during such vacuumtransitions. Physically, these transitions arise from the competing effects ofminimizing the energy for brane nucleation (facilitating a change in flux),versus the energy cost associated with dynamical changes in the periods ofcertain Calabi-Yau 3-cycles. We find that tunneling only occurs when warpingdue to back-reaction from the flux through the shrinking cycle is properlytaken into account.

Conifolds and Tunneling in the String Landscape