During binary fission, dna copies move to opposite ends of the parent cell. this process is most similar to which phase of mitosis?

Anaphase

Explanation:

Anaphase of mitosis is marked by splitting of centromere that joins the two sister chromatids of a chromosome together. Splitting of centromere separates the sister chromatids from each other which then move to the opposite poles of the cell with the help of spindle fibers.  

Likewise, during binary fission, the replication DNA moves to the opposite poles. Hence, this movement of DNA is similar to the anaphase of mitosis.