Step 1: Set the scene.
Meiosis is a special cell division that makes four cells, each with half the chromosome number. We must judge four statements about it.
Step 2: Test statement A.
During meiosis, matching (homologous) chromosomes pair up and swap parts, which is called recombination. This is true, so A is correct.
Step 3: Test statement B.
Crossing over is carried out with the help of enzymes such as recombinase. So it is an enzyme-mediated process, and B is correct.
Step 4: Test statement C.
During the diakinesis stage, the points where chromosomes joined (chiasmata) move toward the ends, called terminalization. So C is correct.
Step 5: Test statement D.
Interkinesis is the short rest stage between Meiosis I and Meiosis II, not between prophase I and prophase II. So D is false.
Step 6: Choose the right set.
The correct statements are A, B, and C, so the answer is A, B, C.
\[ \boxed{\text{A, B, C}} \]