Hi Neale. Thank you for the comprehensive reply. It is so valuable, as I did think about this issue all day and could not come up with a method as yet. I was thinking of taking the time to build a large precise construction square, so I can figure out if the gantry is perpendicular with the y axis rails, but then, in order to get the most precise reading, I needed to have a tool that touches both x and y rails at the same time, and it is a quite a pain for me to build such a tool with enough accuracy, as there is a significant difference in height between this two sets of rails.

Regarding your post, ˇˇThe difficult part is bolting down the first rail absolutely straight.ˇˇ, before doing that, is it not necessary to set the y axis linear bearings/rails absolutely perpendicular to the x axis rails?
All holes for the bearings, rails, steel tubing, aluminium plates, are a bit larger than they were necesary, so sideways adjustement is not a problem, but I.m not sure if I should set the bearings in relation to the x axis first or the y axis rails and do the bearing afterwards.

A precision level cost here 100+ euro, and even if I.m tempted to discuss this option with Santa this year, I.m a bit concerned that, except for this job, I.ll never use it again. Thanks for the tip, though, I did not even know this tool exists until today.