A couple ways to save time. The first one is probably the most practical, the second is an alternative, and the third is just for fun :p
On the first one, you should be holding jump going into the fan. Depending on your positioning, it's possible to do this with holding jump the entire time, but you will probably need to let go of jump in the middle of the fan most of the time.
The second uses a short hop over the second Mannan. You can tap the button to get over him, but it makes it a bit easier to hold jump for a tiny bit. Using the Fireball isn't necessary, but it is safer to do.
The timing on the jump up the fan in the third method is kinda tricky, but you probably shouldn't be doing this in a run anyway :p
![](https://s2.save4k.ru/pic/yGTkZqfopo0/mqdefault.jpg)