The phrase "haul around" can be replaced with numerous synonyms in order to express different shades of meaning. Some potential synonyms include: carry, drag, transport, pull, tug, shift, heave, convey, and move. Each of these terms can be used to convey a similar idea of moving something from one place to another, although the precise connotations may vary. For example, "drag" suggests a slower and more arduous process than "carry," while "tug" implies a more forceful exertion of effort. The choice of synonym may depend on the context of the sentence and the specific effect the writer is hoping to achieve.