keep eye on
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keep (one's)/an eye on (someone or something)
To watch someone or something carefully; to be attentive to someone or something. You need to keep your eye on the soup so that it doesn't bubble over. Sure, I can keep an eye on the baby while you go to the store.
keep one's eye on someone or somethingand have one's eye on someone or something
Fig. to have one's attention directed to someone or something. Please keep your eye on the children while I go to the store. Bill kept an eye on his expenses because he was spending too much money.