The vortex-liquid and vortex-solid phases in single crystals of Bi2Sr2CaCu2O8+δ placed in tilted magnetic fields are studied by in-plane resistivity measurements using the Corbino geometry to avoid spurious surface-barrier effects. It was found that the anisotropy of the vortex-solid phase increases with temperature and exhibits a maximum at T≈0.97Tc. In contrast, the anisotropy of the vortex-liquid phase rises monotonically across the whole measured temperature range. The observed behavior is discussed in the context of dimensional crossover and thermal fluctuations of vortices in the strongly layered system.