Just an Answers enthusiast! In short, the veinules, the pulmonary artery, and all veins except for the pulmonary vein are the blood vessels that carry blood that is rich in carbon dioxide. Unless you want to explain all that, the best answer is veins..The capillaries that carry carbon dioxide back toward the heart are called veinules.The veinules join up to form veins. They eventually connect to the vena cava. The vena cava, which is the largest vein coming from the body, also carries deoxygenated blood, like nearly every other vein.ust an Answers enthusiast! In short, the veinules, the pulmonary artery, and all veins except for the pulmonary vein are the blood vessels that carry blood that is rich in carbon dioxide. Unless you want to explain all that, the best answer is veins..