In Matthew 10:23, he said to the disciples, “When you are persecuted in one town, flee to another. Truly I tell you, you will not finish going through all the towns of Israel before the Son of Man (Jesus) returns“.

Matthew 10:23 is a Matthean addition that limits the duration of the apparent delay. Its redactional character is apparent from its function as the conclusion of the unit in 10:17-23 which was taken from the Markan Olivet discourse (Mark 13:9-13) and relocated here. A sure sign that the Matthean version is redactional of Mark is the doublet (“he who endures to the end will be saved”) in both 10:22 and 24:13. The author brings together the eschatological persecution of the disciples with the instructions in 10:5-15, with 10:23 drawing on 10:14. The author is still thinking of his contemporaries, and not some distant future time.

As for Mark 13:10, the author is probably thinking of Paul’s declaration that the gospel had already spread to all creation (Romans 1:5, 8, 10:16-18, 1 Thessalonians 1:8, Colossians 1:5, 23), and Paul’s mission certainly preceded the disaster of the Jewish revolt and the destruction of the Temple, so the preaching was accomplished first (πρῶτον in 13:10), with Paul indeed giving his testimony before governors and the imperial court in Rome (as in Mark 13:9)

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so, is matthew 10:23 a change created because of the delay in the second visit ? 

mark:

9 ** you do not have permission to see this link **But the one who endures to the end will be saved.

relocated here

¹⁷ Be on your guard; you will be handed over to the local councils and be flogged in the synagogues. ¹⁸ On my account you will be brought before governors and kings as witnesses to them and to the Gentiles. ¹⁹ But when they arrest you, do not worry about what to say or how to say it. At that time you will be given what to say, ²⁰ for it will not be you speaking, but the Spirit of your Father speaking through you.

²¹ “Brother will betray brother to death, and a father his child; children will rebel against their parents and have them put to death. ²² You will be hated by everyone because of me, but the one who stands firm to the end will be saved. ²³ When you are persecuted in one place, flee to another. Truly I tell you, you will not finish going through the towns of Israel before the Son of Man comes.

A sure sign that the Matthean version is redactional of Mark is the doublet (“he who endures to the end will be saved”) in both 10:22 and 24:13. The author brings together the eschatological persecution of the disciples with the instructions in 10:5-15, with 10:23 drawing on 10:14. The author is still thinking of his contemporaries, and not some distant future time.