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Normal-state reentrant behavior is observed in the resistive transition for Bi-2212/2223 intergrowth single crystals. It is found that for a small driving current of 50 μA the resistivity for the intergrowth system exhibits a superconducting transition with zero values at 105 K, which returns to the resistive state at a lower temperature. With a further temperature decrease, the system again becomes superconducting at 92 K. In the case of large driving currents, the reentrant behavior is not found and only a two-step resistive transition is observed. The normal-state reentrant behavior is interpreted using a model where the Josephson coupling between the CuO2 trilayers is weakened by thermally activated resistance between these layers. The two-step transition can be explained by the proximity effect along the ab plane. Our results suggest that due to thermally activated resistance between the superconducting layers in the layered superconductors like Bi-Sr-Ca-Cu-O, the three- to two-dimensional crossover of superconducting behavior may be induced at temperatures much lower than Tc by applying magnetic or electric fields.