The blood vessels dilate to increase the "blood traffic" through the lungs to carry more oxygen to the muscle. The lungs work harder (faster respiratory rate) to increase the rate of oxygen/carbon dioxide exchange in the lungs.
You start to breeze harder and faster and so the heart is working harder. You need more oxygen to continue your exercise, so the blood flow has to increase to bring enough oxygen to the cells. The blood volume didn't increase, it's just running an bit faster through the venes and arteries.
