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After a brief review and a more refined analysis of some relevant analyticityproperties (when going from Minkowskian to Euclidean theory) of the high-energyparton-parton and hadron-hadron scattering amplitudes in gauge theories,described nonperturbatively, in the eikonal approximation, by certaincorrelation functions of two Wilson lines or two Wilson loops near the lightcone, we shall see how these same properties lead to a nice geometricalinterpretation of the crossing symmetry between quark-quark and quark-antiquarkeikonal amplitudes and also between loop-loop eikonal amplitudes. This relationbetween Minkowskian-to-Euclidean analyticity properties and crossing symmetryis discussed in detail and explicitly tested in the first orders ofperturbation theory. Some nonperturbative examples existing in the literatureare also discussed.Comment: Completely revised version with new comments, new references and new  figures; 37 pages + 5 figure

Analyticity and crossing symmetry of the eikonal amplitudes in gauge theories