Passengers must be in possession of the documents necessary for pet transport. Pets that want to accompany their master on holiday in Europe need to have a European passport (which can be acquired from a veterinarian). For identification purposes the animal must have a chip or tattoo.
If you are going to Cyprus, your pet will need an extra preventive treatment against echinococcus (a parasite living in the stomach and intestines) and ticks between 48 hours and 24 hours before departure. This treatment should be mentioned in the passport.
You can find further information on this page or at the veterinarian's where you received the passport.