  Suppose $\mathcal{F}$ is a finite family of graphs. We consider the following
meta-problem, called $\mathcal{F}$-Immersion Deletion: given a graph $G$ and
integer $k$, decide whether the deletion of at most $k$ edges of $G$ can result
in a graph that does not contain any graph from $\mathcal{F}$ as an immersion.
This problem is a close relative of the $\mathcal{F}$-Minor Deletion problem
studied by Fomin et al. [FOCS 2012], where one deletes vertices in order to
remove all minor models of graphs from $\mathcal{F}$.
  We prove that whenever all graphs from $\mathcal{F}$ are connected and at
least one graph of $\mathcal{F}$ is planar and subcubic, then the
$\mathcal{F}$-Immersion Deletion problem admits: a constant-factor
approximation algorithm running in time $O(m^3 \cdot n^3 \cdot \log m)$; a
linear kernel that can be computed in time $O(m^4 \cdot n^3 \cdot \log m)$; and
a $O(2^{O(k)} + m^4 \cdot n^3 \cdot \log m)$-time fixed-parameter algorithm,
where $n,m$ count the vertices and edges of the input graph.
  These results mirror the findings of Fomin et al. [FOCS 2012], who obtained a
similar set of algorithmic results for $\mathcal{F}$-Minor Deletion, under the
assumption that at least one graph from $\mathcal{F}$ is planar. An important
difference is that we are able to obtain a linear kernel for
$\mathcal{F}$-Immersion Deletion, while the exponent of the kernel of Fomin et
al. for $\mathcal{F}$-Minor Deletion depends heavily on the family
$\mathcal{F}$. In fact, this dependence is unavoidable under plausible
complexity assumptions, as proven by Giannopoulou et al. [ICALP 2015]. This
reveals that the kernelization complexity of $\mathcal{F}$-Immersion Deletion
is quite different than that of $\mathcal{F}$-Minor Deletion.
