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Tipsy and Savannah will eventually get along; if they merely 'tolerate' each other, that's fine, and if they become 'friends', that's better. All cats are very wary at first, especially being in a new environment with new humans and new feline they are not familiar with. The first thing I would do at this point is get a Feliway plug in diffuser and put it in the room where they spend the most time. This emits cat calming pheromones that only cats can detect and has no scent to humans. It resembles a plug in air freshener, but is not perfumed.
Next, try the scent transfer method: take a very slightly dampened cloth or paper towel and pet one cat, then the other, then vice-versa; do this frequently throughout the day. This will deposit each cats' scent on the other and make them feel more 'familiar' with each other. You can also take an old t-shirt of yours and pet both cats with it, so YOUR familiar scent is deposited on their fur and this will help make them feel more secure and comfortable.
They should see each other at first, but not really interact. They need to get used to each others' scents and the fact that they both co-exist in this living space. You can offer them cat-healthy treats while they are in the same room, so they see that good things happen when they're together. A good ice breaker is a feather wand or fishing pole toy, with which YOU supervise the play and give them turns trying to bat at the toy and 'catch' it, but then let it go. Note: don't leave this toy alone with them, as small pieces can be chewed off. Put it away after use, where it is inaccessible to them.
I don't believe it is fair for one cat (Tipsy) to be restrained on a leash, when Savannah is not; I also don't believe this is necessary. I understand why you did it, to have more control of the situation and keep Tipsy safe, in case Savannah attacked, but at this point, 3 months in, they should be used to seeing each other in the house and smelling each other. Very important: if you ever choose to use a leash again for either or both cats, make sure it is a leash attached to a body harness and not only attached to a collar, which can damage the neck.
Cats seem to work things out very well on their own, and unless you see extreme fighting and blood/wounds, they will work out their own hierarchy. Typically, there is a dominant and a submissive cat. The fact that Tipsy turned on her back, leaving her belly exposed, shows she trusts Savannah to be a friend and is not afraid of her. A cat will not expose her belly to a predator she fears.
Here are some excellent tips re: new introductions:
I hope things improve soon, after you introduce some of these new techniques and please let me know how things are going. Thanks!
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