Feline infectious anemia is the name for a parasite of the blood, usually transmitted by fleas. It is not transmissible from cat to cat, or via bedding, bowls, etc...
You need to be certain that any fleas are gone from the environment, and that you use a monthly flea preventative on your new cat. Keeping your new cat strictly indoors will aslo help to prevent flea infestation and possible subsequent infectious anemia.
Here's more info on Feline Infectious Anemia:
http://www.marvistavet.com/html/feline_infectious_anemia.html
Good Luck,
Drew
If this answer was helpful, Please click "Accept" so that your deposit can be paid to me, in return for my time spent helping you and your pet.