Anthem House Apartments For Rent . Find anthem apartments for rent that you'll love on redfin. Visit rent.com now for rental rates and other information about this property. Anthem House Apartments in Gainesville, Florida Swamp Rentals from www.swamprentals.com Compare rentals, see map views and save your favorite apartments. Compare rentals, see map views and save your favorite houses. Come see us today and discover luxury apartment living.