  We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski
space given the Euclidean Bethe-Salpeter amplitude -- or alternatively the
Light-Front wave function -- as input. The method is based on the numerical
inversion of the Nakanishi integral representation and computing the
corresponding weight function. This inversion procedure is, in general, rather
unstable, and we propose several ways to considerably reduce the instabilities.
In terms of the Nakanishi weight function, one can easily compute the BS
amplitude, the LF wave function and the electromagnetic form factor. The latter
ones are very stable in spite of residual instabilities in the weight function.
This procedure allows both, to continue the Euclidean BS solution in the
Minkowski space and to obtain a BS amplitude from a LF wave function.
