Accidently deleted some small sized partitions when installing Windows. OSX Partition wont boot
You didn't delete any partition. Instead the MBR got bogus by using Windows' Disk Management tool.

Instead of the MBR you should have a pMBR. After removing the bogus MBR you have to destroy and recreate the GUID partition table:


Boot to Internet Recovery Mode
Open Terminal in the menubar Utilities -> Terminal
Get an overview (especially the gpt command is important!):

diskutil list
gpt -r show disk0

Unmount disk0:

diskutil umountDisk /dev/disk0

Delete the MBR:

dd if=/dev/zero of=/dev/disk0 bs=512 count=1

Destroy the GUID partition table and create a new one:

gpt destroy disk0
gpt create -f disk0

Rebuild all previous GUID partitions:

gpt add -i 1 -b 40 -s 409600 -t C12A7328-F81F-11D2-BA4B-00A0C93EC93B disk0
gpt add -i 2 -b 409640 -s 166939584 -t 53746F72-6167-11AA-AA11-00306543ECAC disk0
gpt add -i 3 -b 167349224 -s 1269536 -t 426F6F74-0000-11AA-AA11-00306543ECAC disk0
gpt add -i 4 -b 168620032 -s 68356096 -t EBD0A0A2-B9E5-4433-87C0-68B6B72699C7 disk0


If you get a resource busy error after one of the steps, just unmount disk0 again with 

diskutil umountDisk /dev/disk0



Depending on your Mac model this will render your Windows installation unbootable. Check one of David Anderson answers how to restore a proper MBR entry to boot Windows if you have a MBR-bootable Mac (in contrary to GUID-bootable Macs since ~2013).