Is every long exact sequence
$$\cdots\to\pi\_{d+1}(B)\to\pi\_d(F)\to\pi\_d(E)\to\pi\_d(B)\to\pi\_{d-1}(F)\to\cdots$$
with topological spaces $F,E$ and $B$, where $F$ is a subspace of $E$ with inclusion map $i$, induced by a Serre fibration $p:E\to B$ ? By "induced" I mean that the maps in the sequence are given by 
$$p\_\*:\pi\_d(E)\to\pi\_d(B)$$
$$i\_\*:\pi\_d(F)\to\pi\_d(E)$$
and the boundary map
$$\partial:\pi\_{d+1}(B)\to\pi\_d(F).$$


If not, what are the conditions under which this is the case?


Thank you!



Is every long exact sequence of homotopy groups induced by a fibration?
Ok, so one counterexample to the other interpretation of the question would be to take a fibration $F\to E\to B'$
And let $B$ be a space with the same homotopy groups as $B'$ but not homotopy equivalent to $B$. Note that $B$ must have at least two non-trivial homotopy groups. 


