Is saying "ahd 'alay" (a covenant upon me) considered a vow, even if a vow was not intended by it?

The phrase "lak alayya ahd" (I have made a promise/covenant to you) is neither a vow (nadhr) nor an oath (yamin), and therefore, nothing is incumbent upon the person who says it. The same applies to phrases like "lak alayya ahd Allah" (I have made a covenant with Allah to you) or "uṭīka ahd Allah" (I give you the covenant of Allah); these are not considered oaths.