Obvious and evident can be interchangeable = it is plain to see.
Overt and Covert are two words that mean the opposite and are often used together, in the field of security surveillance. OVERT= done openly COVERT = not done openly. overt cameras you will see covert cameras will be hidden.
explicit = done, said, commanded or writing openly leaving no doubt.
manifest = clear or obvious to the eye or mind.
All words have a small degree of overlap, but you will find people tend to use them for different situations (although you do not have to).