Check whether two 3x3x3 algorithms are equivalent by simulating their effects and comparing the results. I love this way to simulate these puzzles, no complicated data structures needed.

3x3x3_simulator.py

def sim(alg):
    state = "UF UR UB UL DF DR DB DL FR FL BR BL UFR URB UBL ULF DRF DFL DLB DBR".split()
    for move in alg.split():
        perm = "FLBR FRBL FDBU FUBD URDL ULDR".split()['UDLRFB'.index(move[0])]
        n = 2 + "2'".find(move[-1])
        table = str.maketrans(perm, perm[n:] + perm[:n])
        state = [p.translate(table) if move[0] in p else p for p in state]
    return state

print(sim("D L2 B2 L2 R2 F2 R2 U2 R2 D' U' R' B F L' D R2") == sim("U R B F L D R2"))