From $SARIMA(0,2,1)\times(0,0,1)_{12}$ we have $\phi_0(B)(1-B)^2\Phi_0(B^{12})(1-B^{12})^0 Y_t = \theta_1(B)\Theta_1(B^{12})e_t$, where

$\phi_0(B)=\Phi_0(B^{12})=1$

and

$\theta_1(B)= 1+\theta_1B$,

$\Theta_1(B^{12})=1+\Theta_1B^{12}$.

And the result is

$Y_t-2Y_{t-1}+Y_{t-2}=e_t+\Theta_1(e_{t-12}+e_{t-1})+\theta_1\Theta_1e_{t-13}$

From $SARIMA(0,2,1)\times(0,0,1)_{12}$ we have $\phi_0(B)(1-B)^2\Phi_0(B^{12})(1-B^{12})^0 Y_t = \theta_1(B)\Theta_1(B^{12})e_t$, where

$\phi_0(B)=\Phi_0(B^{12})=1$

and

$\theta_1(B)= 1+\theta_1B$,

$\Theta_1(B^{12})=1+\Theta_1B^{12}$.

And the result is

$Y_t-2Y_{t-1}+Y_{t-2}=e_t+\Theta_1e_{t-12}+\theta_1e_{t-1}+\theta_1\Theta_1e_{t-13}$