Where is the Signature stored in a SegWit transaction? I understand that SegWit makes transaction blockdata smaller, by not storing the signature in the Block, so that can fit more transactions in 1MB. This is because the signature is not anymore stored in the blockchain. The Signature makes nearly 70% of the data weight of the Block. So in a SegWit transaction it is 70% less stored in the Blockchain. But where are the signature stored if not in the Blockchain ?
That's not accurate. The witness is stored in the blockchain.
In the segwit format, the signature is part of the witness, the witness is part of the transaction and the transaction is written to the block in full. Nodes that understand segwit will download and store the complete transaction including the signature.
However, segwit is constructed in a forwards compatible manner. It's made so that it is possible to produce a &quot;stripped version&quot; of a segwit transaction that omits the &quot;witness&quot;. This stripped version is a non-standard valid transaction according to pre-segwit rules. This means that pre-segwit nodes will not propagate it when it is unconfirmed, but accept it when it is included in a block. Segwit-enabled nodes would consider the stripped version incomplete and therefore depend on receiving the complete version of the transaction from another segwit-enabled node.
Since the transaction outputs are part of the stripped transaction (because they are not part of the witness), pre-segwit nodes will come to the same conclusion regarding the ownership of funds by following the stripped blocks as segwit-capable nodes that read the complete blocks.
Part of the criticism of segwit is that pre-segwit nodes will not verify the signature of segwit transactions, as they do not receive the witness and wouldn't know what to do with it. This means that a legacy node might accept an segwit-invalid block until that block is no longer part of the most-work chain-tip. However, such a block would not propagate well on the network, as about 89% of the nodes on the network are segwit-capable. If you're receiving a significant amount of funds from a segwit transaction and are running a segwit-incapable node, you might want to wait for  additional confirmations before taking it at face value. However, for significant amounts that would be a great idea regardless.