I think what you are looking for, actually, is something along these lines:
$(document).on('mouseover', '.hovertip', function() {
// handle your mouseover changes, here
});
$(document).on('mouseout', '.hovertip', function() {
// handle your mouseout changes, here
});
.live, .bind, are all deprecated, AFAIK, which means they'll go away in the future, and you might not want to rely on their continued support.
It would also be far better to replace $(document)
with a selector that's closer to your .hovertip elements, but above them in the DOM nesting, so they can respond to your event, but without forcing jQuery to watch for every event on every element in the whole document. I simply put document in there as an example, as I don't know what the rest of your structure looks like.
http://jsfiddle.net/mori57/qa7py/
As I think about it, I think it's worth pointing out that throwing things to .parent() may not always work out the way you expect, especially if you're modifying the DOM. I think it's far safer to set a higher-level event handler.
If you must use something like the .parent(), I always found more accurate results with .closest(), and giving it a selector also helps the parsing engine narrow its search. You don't want one parent triggering the hover state for /all/ the .hovertips at one time, which could happen in some cases.