Understanding axis

I've been learning the use of axis in transformations and I stumbled on
something that didn't seem to make sense...

local-name( */* )
local-name( */child::* )

return the same values. I would have thought...

local-name( */child::* )
local-name( */*/* )

would be the same (which they aren't).

Could somebody help me reason out why it is this way? This seems to
complicate scenarios where I would only want certain nodes based upon their
children without changing context. For instance, something like:

<xsl:for-each select="*/child::*[local-name()=$v]">
</xsl:for-each>

read as I only want */* where they have a child named $v.

Much thanks in advance.
-Adam

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