At the moment the US price + shipping is still cheaper than buying on an Europe Amazon with free shipping (3 euro cheaper than what amazon.de asks after their price drop).
No, not at all.
Ordering the book at Amazon.com with a delivery address in Europe costs about USD 87.
USD 87 = EUR 77.
USD 87 = GBP 58. Compare this with the amazon.co.uk price of GBP 46.20 (Brits have 0% VAT on books). Erm...
Ordering the book from amazon.co.uk to German delivery address costs £54.45. This includes 7% VAT. Adjustment to Belgian 6% VAT makes £53.95 (i assume shipping costs will remain the same). This is about
EUR 72.
If you pay with credit card you might need to add a fee because of payment in GBP (depending on the terms of your CC institute). Assuming this fee being 2% you will end up with a price of
EUR 73.44 that is being deducted from your CC account.
So, as a European do you really want to order from amazon.com?
Even in the possible best case scenario (i.e., your customs office not collecting VAT) Amazon.com is still more expensive than amazon.co.uk.
Note that the calculated amazon.co.uk prices i wrote in red already include shipping costs and VAT(!).
The meager saving of 3 Euro you mentioned compared to amazon.de you only get if you have a lazy customs office which does not collect VAT, and if there are no additional credit card fees involved. If your customs office is not totally incompetent, it will charge you with the VAT, lifting the amazon.com purchase cost above the amazon.de price.