What Can Be That Bluish Color on my Front Teeth Edges?

Without a picture it would be hard to tell you with 100% certainty but it sound like you are taking about the translucent enamel at the edge of the tooth.  If you have veneers or crowns, the ceramist may have added it, if it is within you natural tooth it is normal unless you find it getting worse which could indicate you are wearing your enamel down and now you are able to see through the layer.
 

I didn't see any pictures you might have sent, but it is very common for anterior teeth to have a "translucent enamel halo" at the edge. Some have it more than others, depending on the thickness & length of the enamel. In fact, a good ceramist will try to duplicate that look on porcelain veneers or crowns. It's a very natural look.

 

Hi A10 in NJ,

Without a picture or seeing you in person, it’s impossible to tell for sure, but most likely the bluish color you see is actually transparency in the enamel. 

Often this comes with wear or thinning of the enamel which is natural with age, or it sometimes appears with over bleaching. 

Unfortunately it is permanent, but it can be corrected with porcelain veneers.

Hope this helps.

Best,

Dr. Alper