The phrase "minding trip" typically refers to looking after something or taking care of a task. Synonyms for this phrase might include "taking care of," "attending to," "managing," "regulating," "overseeing," "supervising," or "sustaining." These words all carry similar meanings, though they may be used in slightly different contexts or imply slightly different levels of responsibility or involvement. Other related phrases might include "keeping an eye on," "watching over," or "monitoring," which all suggest a similar sense of vigilance and attentiveness. Ultimately, the precise choice of words will depend on the specific task or situation being described.