We have performed muon-spin-rotation measurements on the high-temperature superconductorBi2.15Sr1.85CaCu2O8+delta for a range of oxygen stoichiometries. The low-temperature in-plane penetration depth lambdaab was determined as a function of oxygen content. In addition, for each sample the crossover field Bcr, separating the regime of three-dimensional and quasi-two-dimensional vortex behavior, was measured. It is found that Bcr depends only on the penetration depth as Bcr=Phi0/lambda2ab rather than on the superconducting anisotropy gamma. This may be understood in terms of a system of vortices controlled predominantly by electromagnetic interactions. The results are contrasted with other materials, such as HgBa2Ca3Cu4O10+delta, where Josephson coupling plays a more significant role.