Is it possible to have true transparency (without ghost shadows)? Is it possible to have true transparency?

I have modelled a house with four walls and I want to do a section zoom where, at the beginning, I have the walls solid, but one gradually gets transparent.

I have animated a solid and a transparent material through a mix shader, but my problem is that when it's transparent the edges of the walls still have black shadows

I have tried to find some render settings that will remove those "ghost-shadows" but without any success. 

I don't want the "hard clip" like the one that we get with the "restrict rendering".
What is probably happening here is a "Z-fight" between the surface of the transparent wall and that of the opaque one, meaning that since they are overlapping exactly along one of their faces, the render engine is confused as to which one to use for shading calculations.

One may think that a fully white transparent surface wouldn't Z-fight, ...but it does.



As a solution: remove the overlap! Move the surface a tiny bit away (or inside) the opaque wall.