There is a way to teleport back by dying on purpose. To do so you have to abuse the death system that respawns your character to the last place were you were standing upright on a solid ground.
You can land only on flying platforms and commit suicide to warp back to the beginning for example. The other way is to use the Wheel to go somewhere and die without exiting Wheel mode. Death Warps are useful for speedruns, as they allow you to get items in a dead end without having to backtrack.
When you land on a ground, you can enter Wheel mode instantly if you keep the down direction and jump button pressed. In addition to the fact that it saves a bit of time, it's not considered as a new checkpoint for your character when you die. It can be used to extend the possibilities of Death Warps.
There are some small skips in the game but one of them is a large skip that was surely intended by the developers: at the beginning of stage 3 lure the fling enemy above the first falling platform you encounter. Bounce on it to access to the upper part and reveal 2 hidden generators to the left to grab the Extend. From there time your jump to arrive directly in the second half part of the level.