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The electronic band structure probed by angle-resolved photoemission spectroscopy on thin epitaxial La_(2−x)Sr_(x)CuO_(4) films under extreme tensile strain shows anomalous features compatible with c-axis dispersion. This result is in striking contrast with the usual quasi-two-dimensional (2D) dispersion observed up to now in most superconducting cuprates, including relaxed and compressively strained La_(2−x)Sr_(x)CuO_(4) films grown under the same conditions. The data were analyzed using a 3D tight-binding dispersion for a body-centeredtetragonal lattice. We relate the enhancement of the c-axis dispersion to the significant displacement of the apical oxygen induced by epitaxial strain.