Hybridization of Bogoliubov quasiparticles (BQPs) between the CuO$_2$ layers in the triple-layer cuprate high-temperature superconductor Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+delta}$ is studied by angle-resolved photoemission spectroscopy (ARPES). In the superconducting state, an anti-crossing gap opens between the outer- and inner-BQP bands, which we attribute primarily to interlayer single-particle hopping with possible contributions from interlayer Cooper pairing. We find that the $d$-wave superconducting gap of both BQP bands smoothly develops with momentum without abrupt jump in contrast to a previous ARPES study. Hybridization between the BQPs also gradually increases in going from the off-nodal to the anti-nodal region, which is explained by the momentum-dependence of the interlayer single-particle hopping. As possible mechanisms for the enhancement of the superconducting transition temperature, the hybridization between the BQPs, as well as the combination of phonon modes of the triple CuO$_2$ layers and spin fluctuations are discussed.
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