Knot surgered elliptic surfaces without 1- and 3-handles for a (2, 2h + 1)-torus knot

For any positive integers h and n, we show that a knot surgered elliptic surface E(n)T(2,2h+1) for a (2, 2h + 1)-torus knot T (2, 2h + 1) admits a handle decomposition without 1- and 3-handles using a Kirby diagram derived from a Lefschetz fibration on it. As a corollary, an elliptic surface E(1)2,2h+1 has such a handle decomposition.