The relationship here is `predator and prey`. A cat is a predator for a mouse, they hunt and eat them. Now, we need to find the animal that hunts on and eats flies among the given options.

Option 1: Rats do not hunt flies. They are generally herbivores but might show omnivorous tendencies under certain conditions. However, flies do not serve as their primary food source.

Option 2: The term `animal` is too wide and unspecific to be correctly linked with flies in a predator-prey relationship.

Option 3: Spiders are accurate. They are well-known for trapping and eating flies. Hence, just like cats prey on mice, spiders prey on flies.

Option 4: Horses do not hunt or eat flies. They are herbivores who primarily feed on hay and other types of vegetation.

So, the only correct matching option is 3. The spider is to fly as cat is to mouse, creating the representative predator-prey association.