"during meiosis, errors occur during chromosome replication. which term describes the rearranging of genetic material between nonhomologous chromosomes without a net loss or gain of genetic material? "

The term that describes the rearranging of genetic material between non homologous chromosomes without a net loss or gain of genetic material is Translocation.
Chromosomes translocation is an abnormality that results from the rearrangement of parts between non homologous chromosomes.  A gene fusion may be created when the translocation joins two or else separated genes and is normally detected on karyotype of affected cells.