Python 2.7.3 (default, Mar 13 2014, 11:03:55) 
[GCC 4.7.2] on linux2
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>>> a=['dog']
>>> b=a
>>> a
['dog']
>>> b
['dog']
>>> b.remove('dog')
>>> a
[]
>>> b
[]
>>>

When defining a list from another (b=a), in my opinion, I expect that all you do to one doesn't affect to the other one.
However, with the commands .remove & .append I don't see that (the definition b=a is bijective).
Should it work this way?

Thanks

This is a natural consequence of Python using reference semantics.

x = y

just makes x and y references to the same object. For immutable objects like int and str, you'll never notice consequences of this, since changes to the value (x += 1) replace the reference in x with a new reference. But for mutable objects like lists, you need to explicitly copy (shallow or deep) to avoid a dependency of the sort you've encountered.

For the specific case of sequences, the empty slice is the simplest, fastest way to perform a shallow copy:

x = y[:]

For other built-in types, you can often call .copy() or wrap in the constructor:

newdict = olddict.copy() # or dict(olddict)

For more complex cases, the copy module offers shallow and deep copy abilities (via the copy and deepcopy function) for arbitrary data structures.

Short answer: This is not a bug. Run through one of the comprehensive Python tutorials on the net (or in Learning Python); reference semantics and their fairly varied consequences are covered in detail in most of them.