One God revealed to us in three persons. Like you said no analogy is perfect but water, ice and water vapor are all still ferfectly H2O.
I have a feeling that God is so immensely incomprehendable to the human mind. The finite trying to comprehend the infinite! Actually impossible and even if we think we understand I bet this person will only set straight when we see Him face to face. The Bible says there is One God. The Bible show clearly the Father, the Son and the Holy Spirit is God.