zeigen vs. ziehen

I've always been attracted to words beginning with letters at the end of the alphabet, like z. Those sections were always shorter in the dictionary, inviting one to master the entire section with their esoteric words. Germans seem more democratic when distributing common words to the letters of the alphabet. It would be a rare day when I would eat zucchini while watching zebras at the zoo. But in Germany, at the end of a meal, we "zahlen" (pay), either "zusammen" (together) or "getrennt" (separately). And we may "ziehen" (pull) the door to exit.

In my German - English dictionary, there is only one English verb starting with z, to zip. In German, there are many more, and somehow zeigen and ziehen and all their derivatives are mixed in my head. Maybe it is because they have a sense of mirror opposition, with the flipping of the "e" and "i" and rotational flip of the "g" and "h". Anyway, I attempt to straighten them out here.

zeigen - to show
ziehen - to pull

There you go. But it's not so simple. First, here are some derivatives of zeigen:

anzeigen - to announce
die Anzeige - the advert
aufzeigen - to point out
vorzeigen - to exhibit

You will notice that most of these variations have the same theme as the base verb, but the differences in tone are not perfectly clear on leo, so they might have to be the subject of a different post.

On the other hand, leo shows that ziehen is used much like the English word pull, with figurative and literal meanings. One uses "ziehen" to heave, tow, and to be attracted to (with "sich"). Apparently one uses ziehen to also describe brewing tea and cultivating crops. So it is no surprise that derivatives of ziehen cover broad meanings:

ausziehen - to extract
anziehen - to activate; to tighten
abziehen - to distill, skim; to peel off
beziehen - to procure (especially used for types of income); to upholster
erziehen - to raise a child
über jmdn herziehen - to badmouth someone
hinziehen - to prolong
verziehen - to distort, pucker (one's face)
vorziehen - to pull from behind; to prefer (with accusative and dative nouns to show what is preferred over what)
vollziehen - to fulfill; to execute (a law)
zuziehen - to pull together (curtains); to contract a disease (with sich)

ausziehen - to move out
umziehen - to move house

sich anziehen - to dress
sich umziehen - to change clothes