New Zealand Law
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Under a typical cross lease if you ask for consent for matters like this, then if the neighbour refuses you need to arbitrate to resolve the impasse. If his rejection is unreasonable, then under the usual lease terms, he would be required to consent. The issue will be if his concern about the sun shading his property is real or exaggerated. If he is being unrealistic then the arbitration will go against him. However the arbitration can be be, like any litigation, fairly expensive
That is the problem with cross leases, because you need the other cross lease owners consent for any additions. The deck may not be unreasonable however although the fence may be if it will cause shade. And you can plant a hedge on your side of the boundary, bearing in mind that if this does shade his property unduly, he could force trimming to minimise the shading.
There are fence designs which would not cause shade but provide protection, and he likely could not object to that in an arbitration however