hmm...never really thought about that, so I tried it out. My tongue lightly touches my teeth for "anthrax," and somewhere on or just behind or, probably, on the "dental ridge(?)" for "answer." The difference in sound is very slight

Since I know zilch about linguistics I'm admittedly way out of my depth here, but it seems to me that the placement of the tongue is "attached" to the sound that follows (th or s), not to the n sound. Or is it not possible to isolate the n sound from the surrounding letters?