東奔西走（とうほんせいそう） is to run here, there, and everywhere.

「東奔西走」（とうほん せいそう） is to run here, there, and everywhere because you are so busy on business or for some purpose that you cannot stay in a place.

「奔走」（ほんそう） and 「南船北馬」（なんせん ほくば） are synonyms.