There are few options here. Do you need to animation those lines (move their positions each frame) or not?
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use mesh generation as @yaustar suggested. You can see how engine’s cylinder is generated here
https://github.com/playcanvas/engine/blob/5b82eb92c59e34e5110b7534bdfd384db73f76e1/src/scene/procedural.js#L662 -
export a long cylinder tube with skinned bones inside it from Maya or similar, then you can change transforms of those bones to change its shape. Animated textures on top sounds perfect. You could even generate a mesh using function above, and and add bone info to it from code, but that might be bit more tricky.
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if you need to animate connection going from A to B, to move to C to D, you could use morphing as well. http://playcanvas.github.io/#graphics/mesh-morph-many.html uses cylinder generated with function mentioned above, and creates morph targets that expand disks out of it.
If you need this to run on PC or with not large number of connections (100 or so), I’d go for option 2, if you need tons of these, option 1 could be done much more performant.