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The formalism developed elsewhere for the theoretical description of the dynamics involved in the heavy nuclei fusion is applied in this paper to study the history of the fusion of two identical heavy nuclei experiencing central collision. The evolution of the shape and of the temperature of symmetrical fusing systems is studied. The role of the elastoplasticity of nuclear matter in the nonmonotonical changes of the shape is elucidated in this way. A tentative explanation of the extra push phenomenon is given in terms of the competition between elastic properties of fusing systems driving to the re-separation of colliding nuclei and the dissipative (plastic) properties of nuclear matter transforming the energy of collective motion into the energy of statistical excitation and thus leading to the fusion. The fingerprints of the heavy-nuclei fusion history as it is depicted by the model are traced in the anisotropy of the dipole and quadrupole γ-radiation emitted during the fusion. The parallels in the description of the fusion dynamics given by the simple model used in this paper and by the more fundamental approaches based on the kinetic equation are emphasised.