  In the third Galactic quadrant (180 < l < 270) of the Milky Way, the Galactic
thin disk exhibits a significant warp ---shown both by gas and young stars---
bending down a few kpc below the formal Galactic plane (b=0). This warp shows
its maximum at 240, in the direction of the Canis Major constellation. In a
series of papers we have traced the detailed structure of this region using
open star clusters, putting particular emphasis on the spiral structure of the
outer disk. We noticed a conspicuous accumulation of young star clusters within
2-3 kpc from the Sun and close to b=0, that we interpreted as the continuation
of the Local (Orion) arm towards the outer disk. While most clusters (and young
stars in their background) follow closely the warp of the disk, our decade-old
survey of the spiral structure of this region led us to identify three
clusters, Haffner~18(1 and 2) and Haffner~19, which remain very close to b=0
and lie at distances (4.5, 8.0, and 6.4 kpc) where most of the material is
already significantly warped. Here we report on a search for clusters that
share the same properties as Haffner~18 and 19, and investigate the possible
reasons for such an unexpected occurrence. We present UBVRI photometry of
5~young clusters, namely NGC~2345, NGC~2374, Trumpler~9, Haffner~20, and
Haffner~21, which also lie close to the formal Galactic plane. With the
exception of Haffner~20, in the background of these clusters we detected young
stars that appear close to b=0, and are located at distances up to 8 kpc from
the Sun, thus deviating significantly from the warp. These populations define a
structure that distributes over almost the entire third Galactic quadrant. We
discuss this structure in the context of a possible thin disk flaring, in full
similarity with the Galactic thick disk.
