Regarding the mention of Caiaphas in the stories, it really is interesting. Mark the first has a generic "High Priest". Luke also leaves the High Priest unnamed in the arrest story. Matt names the High Priest as Caiaphas. The writer of John on the other hand originally named the High Priest as Annas but later efforts to harmonize the stories led to the insertion of lines that have Jesus brought to and tried by High Priest Annas who then hands him over to High Priest Caiaphas. The text reads easily without the insertions:
12 Then the detachment of soldiers with its commander and the Jewish officials arrested Jesus. They bound him 13 and brought him first to Annas,who was the father-in-law of Caiaphas, the high priest that year. 14Caiaphas was the one who had advised the Jewish leaders that it would be good if one man died for the people.(Reference to 11:49,50 an obvious interruptive addition)
15 Simon Peter and another disciple were following Jesus. Because this disciple was known to the high priest, he went with Jesus into the high priest’s courtyard, 16 but Peter had to wait outside at the door. The other disciple, who was known to the high priest, came back, spoke to the servant girl on duty there and brought Peter in.
17 “You aren’t one of this man’s disciples too, are you?” she asked Peter.
He replied, “I am not.”
18 It was cold, and the servants and officials stood around a fire they had made to keep warm. Peter also was standing with them, warming himself.
19 Meanwhile, the high priest questioned Jesus about his disciples and his teaching.
20 “I have spoken openly to the world,” Jesus replied. “I always taught in synagogues or at the temple, where all the Jews come together. I said nothing in secret. 21 Why question me? Ask those who heard me. Surely, they know what I said.”
22 When Jesus said this, one of the officials nearby slapped him in the face. “Is this the way you answer the high priest?” he demanded.
23 “If I said something wrong,” Jesus replied, “testify as to what is wrong. But if I spoke the truth, why did you strike me?” 24Then Annas sent him bound to Caiaphas the high priest.25 Meanwhile, Simon Peter was still standing there warming himself. So, they asked him, “You aren’t one of his disciples too, are you?”
He denied it, saying, “I am not.”
26 One of the high priest’s servants, a relative of the man whose ear Peter had cut off, challenged him, “Didn’t I see you with him in the garden?” 27 Again Peter denied it, and at that moment a rooster began to crow.
28 Then the Jewish leaders took Jesusfrom Caiaphasto the palace of the Roman governor. By now it was early morning, and to avoid ceremonial uncleanness they did not enter the palace, because they wanted to be able to eat the Passover. 29 So Pilate came out to them and asked, “What charges are you bringing against this man?”
The abundant manuscripts variations in this section reveal an unsettled attempt to harmonize with Matthew.
In short, the progression of a generic High Priest in Mark was interpreted as Annas by the writer of John but Caiaphas by the writer of Matthew. John was then interpolated to try to harmonize but this still creates contradictions and the strange use of the term High Priest for both men in the same paragraph.