  We initiate an in-depth study of pattern avoidance on modified ascent
sequences. Our main technique consists in using Stanley's standardization to
obtain a transport theorem between primitive modified ascent sequences and
permutations avoiding a bivincular pattern of length three. We enumerate some
patterns via bijections with other combinatorial structures such as Fishburn
permutations, lattice paths and set partitions. We settle the last remaining
case of a conjecture by Duncan and Steingr\'imsson by proving that modified
ascent sequences avoiding 2321 are counted by the Bell numbers.
