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Within a covariant perturbative field-theoretical approach, the wave-packet modified neutrino propagator is expressed as an asymptotic expansion in powers of dimensionless Lorentz- and rotation-invariant variables. The expansion is valid at high energies and short but macroscopic space-time distances between the vertices of the proper Feynman macrodiagram. In terms of duality between the propagator and the effective neutrino wave packet, at short times and distances, neutrinos are deeply virtual and move quasiclassically. In the lowest-order approximation, this leads to the classical inverse-square dependence of the modulus squared flavor transition amplitude and related neutrino-induced event rate from distance $L$ between the source and detector, and the above-mentioned asymptotics results in the corrections to the classical behavior represented by powers of $L^2$. This is very different from the long-baseline regime, where similar corrections are given by an asymptotic expansion in inverse powers of $L^2$. However, in both short- and long-baseline regimes, the main corrections lead to a decrease in number of neutrino events.