The phrase "nose out" is commonly used to describe a situation where one person or thing is slightly ahead of another. There are several synonyms for this phrase that can be used interchangeably in different contexts. For example, "edge out" implies that the lead is marginal, while "outpace" suggests a significant difference in speed or efficiency. "Outstrip" can also be used to mean the same thing, implying that one person or entity has surpassed another. Similarly, "overtake" and "outmaneuver" both imply a strategic advantage that allows one person to pass the other. Whichever synonym is chosen, they all convey a sense of one person or thing being ahead of another by a small or significant margin.