Removing intersection on pipes

I was modeling a Klein Bottle and end up in this type of problem after doing Solidify:

I managed to remove the intersections on the Klein duplicating the surfaces and doing Boolean operations with a lot of manual deleting afterwards.

Now I am trying to find a better approach for this problem. I think the easiest solution would be to duplicate both pipes and separate them, after that doing a Intersect Boolean and a Difference in sequence; but it is not removed completely. How it is possible to fix this?

Edit: This pipe problem is a simplification of the Klein. It not about the steps to create pipes, but to fix the mesh obtained by complex XYZ Math Surface:

• maybe check this answer: blender.stackexchange.com/questions/193962/… Commented Sep 6, 2021 at 8:17
• Commented Sep 6, 2021 at 10:37
• Thank you for the answers, but its not for this case. A added some pics to show the Klein Bottle which is the original problem. Commented Sep 6, 2021 at 11:15
• As i said before , it's always best to learn topology instead of bein screwed , or misguided. here is how to make a klein bottle with true thickness in blender youtube tutorial that i made while im not a youtuber . I hope you learn some thing out of it but you NEED to learn topology and study about that . Youtube link : https://youtu.be/hEr0oIXT-0Y pic ![enter image description here](i.sstatic.net/n0J8W.png) Commented Sep 8, 2021 at 7:55
• Nice video, thanks for sharing ^^ Commented Sep 10, 2021 at 0:17

Here is my approach from long ago, although I would do a better job with the angles now:

• Create an UV sphere.
• Delete the top and bottom vertices.
• Extrude a 'column' from the top into the sphere.
• Subdivide one of the faces in the sphere enough times to create a circle.
• Delete all of the faces inside that circle.
• Bridge edge loops between the previous column and the new circle.
• Bring a column around from the bottom to the same circle, by extruding and rotating.