startup and start are sometimes interchangable: "I always start up/start my car five minutes before I leave in the winter so it warms up." take up ~ to begin an activity that has continued or will continue for a long time.: "I decided to take up Spanish= I decided to start learning Spanish." "I took up football when I was nine.= I started playing football when I was nine." Notice that the sentence with "to start" usually needs another verb, and also that here "start up" cannot be used instead of "start". take up~ to present a problem to: "I was having a problem with one of my colleagues, so I took it up with my boss." "take up" can have other meanings too, ("I took up the carpet before the party so that it wouldn't get dirty." ) and whether it is right to use it depends on the circumstances.

Can you be more specific in your question? Like where do you want to use the word? Give a statement for example