Jesus promises that those who are thirsty can drink from Jesus. Those who drink/believe not only have their thirst assuaged. They become springs of refreshing, living water - John tells us the water is the Spirit (John 7:37-39).
But living water is not only refreshing water. Most of the time, “living water” is the running water needed for purification (Leviticus 14:5-6, 50-52; 15:13; Deuteronomy 21:4; the NASB translates “running water,” but the Hebrew is the rhyming hamayim-hachayyiym).
Jesus promises that those who receive the Spirit by trusting in Him become springs of purifying water.
This is a complete reversal of the old covenant, when pollutions flowed from the “belly.” For those who are in the flesh, outflows defiled; those filled with the Spirit flow with the living Spirit to cleanse the world.