Okay, disregard the local one.
You will always see the last saved version on your machine.
This is an instant change so you will see it the instant you change it.

However it can take a little while for the change to happen over the web because you have to upload the file to your host's servers and then have it fed back to your machine (or anyone viewing the page's machine) again.
This [I]should[/I] also be instant but isn't and there are a number of factors which may affect it.
It could be a delay in your host updating your space, it could be a delay in your machine accepting the updated info back from your own site (remembering that the file on your own machine is a separate and independent file from the one on your webspace, only sharing a relationship through being a copy of it, in some form or other).

I have suffered delays of several hours with the host of my own web site (ntl) on occasions. It's very frustrating, but usually it's an instant transition and complaining to ntl takes more effort than living with it. Sign of todays times I'm afraid.