  Geometric aspects of the filtration on classical links by k-quasi-isotopy are
discussed, including the effect of Whitehead doubling, relations with Smythe's
n-splitting and Kobayashi's k-contractibility. One observation is:
\omega-quasi-isotopy is equivalent to PL isotopy for links in a homotopy
3-sphere (resp. contractible open 3-manifold) M if and only if M is
homeomorphic to S^3 (resp. R^3). As a byproduct of the proof of the "if" part,
we obtain that every compact subset of an acyclic open set in a compact
orientable 3-manifold M is contained in a PL homology 3-ball in M.
  We show that k-quasi-isotopy implies (k+1)-cobordism of Cochran and Orr. If
z^{m-1}(c_0 + c_1 z^2 + ... + c_n z^{2n}) denotes the Conway polynomial of an
m-component link, it follows that the residue class of c_k modulo
gcd(c_0,..,c_{k-1}) is invariant under k-quasi-isotopy. Another corollary is
that each Cochran's derived invariant \beta^k is also invariant under
k-quasi-isotopy, and therefore assumes the same value on all PL links,
sufficiently C^0-close to a given topological link. This overcomes an algebraic
obstacle encountered by Kojima and Yamasaki, who "became aware of impossibility
to define" for wild links what for PL links is equivalent to the formal power
series \sum \beta^n z^n by a change of variable.
