If $X$ is a simply connected space and $\alpha\in\pi_n(X)$ and $Y=X\cup_{\alpha} e^{n+1}$.
and $(\wedge V,d)$ be the minimal model for $X$,then $(\wedge V\oplus \mathbb{Q}
u,d)$ is a commutative model for $Y$,
which we denote by $M_\alpha$.
If $f\colon X\rightarrow X_1$
and $Y=X\cup_{\alpha}e^{n+1}$ and $Y_1=X_1\cup_{f^*(\alpha)}e^{n+1}$,then we have a map $g\colon X_1\rightarrow Y_1$ and the 
following commutative diagram (1)

 \begin{array}{lll}
  X  \rightarrow Y\\
  f\downarrow  \downarrow g\\
  X_1  \rightarrow Y_1

 \end{array}


Now,if $(\wedge V_1,d)$ is the minimal model for $X_1$ and so $(\wedge V_1\oplus
\mathbb{Q}u,d)$ is a commutative model for $Y_1$ and if $\phi\colon
(\wedge V_1,d)\rightarrow (\wedge V,d)$
be the Sullivan representative for $f$,then we have induced map $\psi$ from
 $(\wedge V_1\oplus\mathbb{Q}u)$ to $(\wedge V\oplus\mathbb{Q}u,d)$which is $\phi$
 on $(\wedge V_1)$ and identity on $u$.\\
Then we have the following diagram (2)---\\
\[
 \begin{array}{lll}
  (\wedge V_1\oplus\mathbb{Q} u,d) & \rightarrow (\wedge V_1,d)\\
  \psi\downarrow        & \downarrow \phi\\
  (\wedge V\oplus\mathbb{Q}u,d)  & \rightarrow (\wedge V,d)\\
 \end{array}
\]

Now,my questions are--
a)Is $\psi$ a commuatative model for $g\colon Y\rightarrow Y_1$?
b)Is (3) a commutative model for (2)?