> how can I erase this edge to obtain a smooth unique surface here ?

it's not if there is a line(s), that want say that the surface are not smooth for a renderer engine!

If you disable in the Browser Visibility of Edges, you can see that these surfaces are some smooth ;)

If you want absolutly no line you must repair your object!
Verify that you have not Points who are not necessary!

The more easy is Copy Past from the original some parts and reconstruct them ;)

If you have 2 same curves kill one and copy move the last for be sure that they are not fliped!

Then at the end kill false original parts and assemble with news :)



Ps Don't put your object with any orientation in the floating space
because we must rotate it and past it on the gride
for more easy to work on it ;)
(times won)