I just thought I'd add to this thread, if you do decide to allow the father to visit (I'd personally give him a couple of chances to get over, the cost of the flights to see his daughter makes it seem like he is actually putting in some effort!) then get some pictures, show LO the pictures regularly and explain to her that that is her daddy, he can't see her very often because he lives so far away... My brother and sister (dad & step-mum's son and daughter) recognise me because of this, I visited a few times when they were small (living in the UK) then they went to live in Spain, came back and I saw them once or twice, and now I'm living in America... My dad and stepmum frequently show them pictures of all their family living in different parts of the world, so they KNOW who they are and recognise them and understand why they can't see them often irl. They also use Skype for some people (my aunt and cousin (who is the same age as my sister, 2) mostly) so the kids can interact more and see their family, despite being so far away, and get a chance to talk to them.
Just an option to consider, it's obviously up to you what you decide to do, but I personally in this situation would want my daughter to know her father, even if he's not around much...if he made the effort to come over even once a year, spend the airfares etc and talk to her on the phone/webcam etc...it can be worth it. Maybe he needs to prove he really is devoted and can be a decent guy before you feel comfortable, it's natural to want to protect your daughter from possible hurt, but as someone else mentioned if she finds out later on that she could have seen daddy and you didn't allow it...it could come back on you.
Just some stuff to consider, I'm in no position to comment on the situation, because I obviously don't know it well...but just my personal opinion and experience...hope something in there was perhaps a little useful!!!
Good luck for figuring out a solution that you're happy with and I agree he needs to stop pestering your mother, but maybe this shows he really does want to be involved?
xx