What was the relationship between Annas and Caiaphas?
Annas was the father-in-law of Caiaphas. Luke names them together as high priests, and Acts places them together on the council. John 18:13; Luke 3:2; Acts 4:6
What the Bible says
John 18:13
And they led him away to Annas first, for he was father in law to Caiphas, who was the high priest of that year.
Luke 3:2
Under the high priests Annas and Caiphas; the word of the Lord was made unto John, the son of Zachary, in the desert.
Acts 4:6
And Annas the high priest, and Caiphas, and John, and Alexander, and as many as were of the kindred of the high priest.
Douay-Rheims Bible (Challoner revision), public domain.