I read lots questions about what covariance is and I found out that, according to this topic Lorentz invariance of the Minkowski metric, we say an object is covariant if it doesn't take the same value on every frame of reference, but the different values are related in a well defined way: the components of a covariant object must satisfy the tensors transformation rule.
I understand these definitions but at the same time I heard many times about covariance of an equation. I tried to figure out what is a covariant equation and I noticed that if I have an equality where right and left terms are covariant objects than the equation remains true when I change the frame of reference because both sides transform equally. So i was tempted to say en equation is covariant if it's between covariant objects. On the other hand there are some equations that are said to be covariant but doesn't respect this definition. For example the equations of motion when the frame of reference is changed remains true but they are not made of objects that are covariant.