thank you everyone for the great suggestions.
Just to make it clear, I have to print the map on paper 100cmX140cm, the leaflet version was just an example for the paths
I did some test with offset but working only with ArcGIS and QGIS, I have troubles choosing the right offset in order to match lines especially in corners.
I will try some transparency overlap but, being 4 colours, I'm afraid everything get messed up.
I did try some overlapping https://www.dropbox....qpltv3/test.png and then use distance labels to show the underneath path, but I don't particularly like it.
As for the offset inspired to transportation maps, my problem, beside the graphic problem above mentioned, I still have the problem to cover up streeets names
THANKS AGAIN for the great discussion, full of suggestions and inspirational link