a diffeomorphism on a 3-manifold

Question

Assume we have an embedded torus $T=S^1\times S^1$ in $3$-manifold $M$. We construct a diffeomorphism $f$ of $M$ as follows: Take a neighborhood $T\times I$ of the torus and set $f(\theta,\phi,t)=(\theta,\phi+t, t)$, for $0\leq\theta,\phi,t\leq2\pi$ (if $\theta$ and $\phi$ are meridian and longitude directions, the diffeomprphism can be thought of as a longitudinal twist) and extend $f$ as identity outside this neighborhood. Is $f$ isotopic to identity? If not, how can we see the effect of this diffeomorphism on, for instance $H_1(M)$, in case $T$ tubes around a surgery curve?