The phrase "crosses over" implies movement, transition or passing from one place, idea, or activity to another. The antonyms that can be associated with crosses over include stay, remain, stabilize, and settle. These words denote actions that are the opposite of crossing over. When you stay, you don't move. When you remain, you maintain your present position. Stabilizing means to become balanced or steady, whereas settling involves establishing roots in a particular place or situation, rather than moving away from it. These antonyms offer a contrast to the concept of transition, providing options that emphasize stability, consistency or permanence.