Which preposition to use with housekeep

with Occurrences 4%

If Mary counts on my money to begin housekeeping with, she'll find herself mistaken; for not one penny shall she have, married or single, and you may tell her so.

in Occurrences 2%

Housekeeping in a flat, should the owner so will it, is ever conducive to economy, and life in a French provincial town is simple and unconventional.

on Occurrences 2%

He began housekeeping on a scale of regal magnificence.

Which preposition to use with  housekeep