<human>: I've had my 5 year old cat now for 4 years, and she's been the most wonderful, sweetest kitty. Two months ago, another female (around 3 or 4 years) required a new home urgently, so I took her in. 

Unfortunately, the new female and my old cat aren't getting on at all. I did 3 weeks of keeping them separate spaces and feedings behind a door, with occasional glimpses of each other. I've done two weeks of them having more and more time to have the whole house between the two of them, and for the most part they ignore each other. Now I have them both out all the time. Feeding time is fine, even with them close together.

However, if one of the cats surprises the other (one going upstairs for example), the old cat hisses and growls loudly, and the new cat puts on a merry chase round the house till the old cat has a tail resembling a christmas tree. They had one bad fight at the beginning with fur actually flying and real bites, but that was three weeks ago. After that little spat they were back to being separate for a while.

I think I'm doing everything right with these two, but I'm still keeping them separate while I am out of the house, and it's beginning to get tiresome. Is it safe to leave them alone? What could I do differently to help this process along? I swapped scents at the beginning, kept them separate over and over, spray water when they chase, feed them together, and I keep a whole dry food and water station in each's territory. They each have their own litter as well, to prevent them from fussing over resources.

Could you distill the essence of the text into 1-3 sentences?
<bot>: New cat chases growling old cat, done everything I can, has been two months and still no progress, need to leave house without locking them up eventually.